Business Mathematics Jerome Chapter 06

McGraw-Hill Ryerson©

6 - 1Simple

Interest

Simple

Interest 66 66

Chapter

6McGraw-Hill Ryerson©

IISS imple nterest


6 - 2Simple

Interest

Simple

Interest 66 66

Calculate

Learning ObjectivesLearning

ObjectivesAfter completing this chapter, you will be able to:

… interest, maturity value,

future value, and present value

in a simple interest environment

… details of the amount and timing of payments in a time

diagram

… the equivalent value on any date of a single

payment or a stream of payments, and

Present

LO-1LO-1

LO-2LO-2


6 - 3Simple

Interest

Simple

Interest 66 66

Borrower

Example: LoanExample: Loan

Lender

PartiesParties

Lends the PrincipalLends the Principal Borrower OWES (Debt) to Lender

Borrower OWES (Debt) to Lender

LO-1LO-1


6 - 4Simple

Interest

Simple

Interest 66 66

BorrowerLender

Earns (Income) from Borrower

i.e. Interest on the Principal

Earns (Income) from Borrower

i.e. Interest on the PrincipalBorrower pays

Interest to Lender

Borrower pays Interest to Lender

Rate of Interest: Simple Interest …Calculated on an ANNUAL or

per annum (pa) basis

Simple Interest …Calculated on an ANNUAL or

per annum (pa) basis

Example: LoanExample: Loan


6 - 5Simple

Interest

Simple

Interest 66 66ExamplesExamples

Invest $1000 at 10% simple interest for one year.

Interest earned is?

Principal X Interest Rate $1000 *10% = $100

Invest $1000 at 10% simple interest for six months.

Interest earned is?

Principal X Interest Rate $1000 * 10% $50/2 =

=

=


6 - 6Simple

Interest

Simple

Interest 66 66

Invest $1000 at 10% simple interest for three months

Interest earned is?Principal X Interest Rate = $1000 X 10% $25

Invest $1000 at 10% simple interest for one month.

Interest earned is?

Principal X Interest Rate = $1000 X 10% $8.33/12 =

/4 =

ExamplesExamples


6 - 7Simple

Interest

Simple

Interest 66 66

Up to this point we have taken months to represent 1/12th of a year, i.e. each month is treated as having the same number of days!

Would it not be more accurate to calculate the interest due or payable based on the actual number of days

in each month?


6 - 8Simple

Interest

Simple

Interest 66 66 Yes, it would! In fact, interest continues

to accumulate as each day passes!

Invest $1000 at 10% simple interest for 30 days!

Interest earned is?

ExampleExample

Principal x Interest Rate = $1000 *10% * 30

Year = 365 days or 366 in a Leap YearYear = 365 days or 366 in a Leap Year

$8.22=365


6 - 9Simple

Interest

Simple

Interest 66 66

trPI

“What is the formula that can be used to calculate SI?”

Principal Interest Rate Time

Four Elements are involved …Four Elements are involved …

Interest

Formula Formula

Principal Amount (loan or

investment)

Principal Amount (loan or

investment)

Annual Rateof SI

Annual Rateof SI

Amount (paid or received)

Amount (paid or received)

Time period …expressed as a fraction or a multiple

of a year

Time period …expressed as a fraction or a multiple

of a yearI = Prt


6 - 10Simple

Interest

Simple

Interest 66 66

Calculate the Interest earned on $5000

invested at 4% for 7 months.

Formula Formula I = Prt

I = P * r * t $5000 *

.04 * 7 /12

I = $116.67I = $116.67


6 - 11Simple

Interest

Simple

Interest 66 66

“I may need to invest or need a loan for a number

of days rather than a complete

month.”

“How do I calculate the

time between the

starting date and the ending date?”


6 - 12Simple

Interest

Simple

Interest 66 66

Add up the days according to the days covered by the specific months.Include either

the FIRST date or the LAST

date when doing this calculation!

Include either the FIRST date

or the LAST date when doing this calculation!

Use a Number of Days TABLE

Use the TI BAII Plus calculator!

There are three methods that can be used to

calculate the number of days:


6 - 13Simple

Interest

Simple

Interest 66 66

Method 1.Method 1.

What is the interest earned on $5000 invested from Oct. 11th to Dec.

29th at 4.5%?

Calculating the Number of Days

Oct 11th to end of month = 20

Days

Nov Total month =

30

Dec From 1st to 29th

of month = 29 79 79 Includes the last date


6 - 14Simple

Interest

Simple

Interest 66 66

JanMar

MayJuly

FebAprJun

Spaces are ALL 30 days except for February which can be either

28 or 29 days in a Leap year!

Aug Oct Dec

Nov

Sept

The “Hand Calculator!”The “Hand Calculator!”

Knuckles are ALL 31 days


6 - 15Simple

Interest

Simple

Interest 66 66

Thirty days has September,April, June and November.

All the rest have 31,

but February with just 28 days clear

plus one more in each leap year!


6 - 16Simple

Interest

Simple

Interest 66 66Day of Month

TABLE 6.2The Serial Number of Each Day of the YearJan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

1 32 60 91 121 152 182 213 244 274 305 3352 33 61 92 122 153 183 214 245 275 306 3363 34 62 93 123 154 184 215 246 276 307 3374 35 63 94 124 155 185 216 247 277 308 3385 36 64 95 125 156 186 217 248 278 309 3396 37 65 96 126 157 187 218 249 279 310 3407 38 66 97 127 158 188 219 250 280 311 3418 39 67 98 128 159 189 220 251 281 312 3429 40 68 99 129 160 190 221 252 282 313 34310 41 69 100 130 161 191 222 253 283 314 34411 42 70 101 131 162 192 223 254 284 315 34512 43 71 102 132 163 193 224 255 285 316 34613 44 72 103 133 164 194 225 256 286 317 34714 45 73 104 134 165 195 226 257 287 318 34815 46 74 105 135 166 196 227 258 288 319 34916 47 75 106 136 167 197 228 259 289 320 35017 48 76 107 137 168 198 229 260 290 321 35118 49 77 108 138 169 199 230 261 291 322 35219 50 78 109 139 170 200 231 262 292 323 35320 51 79 110 140 171 201 232 263 293 324 35421 52 80 111 141 172 202 233 264 294 325 35522 53 81 112 142 173 203 234 265 295 326 35623 82 113 143 174 204 235 266 296 327 35724 55 83 114 144 175 205 236 267 297 328 35825 56 84 115 145 176 206 237 268 298 329 35926 57 85 116 146 177 207 238 269 299 330 36027 58 86 117 147 178 208 239 270 300 331 36128 59 87 118 148 179 209 240 271 301 332 36229 88 119 149 180 210 241 272 302 333 36330 89 120 150 181 211 242 273 303 334 36431 90 151 212 243 304 365

12345678910111213141516171819202122232425262728293031

363

284Oct 11

Dec 29

= 79 Days= 79 DaysMethod 2.Method 2.

54


6 - 17Simple

Interest

Simple

Interest 66 66

12.2902

Using… Texas Instruments BAII PLUS

i

Days Between DatesDays Between Dates

2nd

CPT

Enter

Method 3.Method 3.

Example 1.Example 1.

Calculate… the interest

earned on $5000

invested from Oct. 11th

to Dec. 29th, 02 at 4.5%.

Start

DBD = 79 Date

10.1102 Enter


6 - 18Simple

Interest

Simple

Interest 66 66


Calculate the Interest earned on $5000 invested

at 4.5%

for ? .

79 Days

I =$5000*.045 * 79/365

I = $48.70I = $48.70


6 - 19Simple

Interest

Simple

Interest 66 66

Method 1.Method 1.

What is the interest earned on $5000 invested from Nov 30th, 02 to Jan

6th, 03 at 4.5%?

Nov 30th to end of month = 0

Days

Dec Total month =

31

Jan From 1st to 6th

of month = 6 37 37

Includes the last date



6 - 20Simple

Interest

Simple



1 32 60 91 121 152 182 213 244 274 305 3352 33 61 92 122 153 183 214 245 275 306 3363 34 62 93 123 154 184 215 246 276 307 3374 35 63 94 124 155 185 216 247 277 308 3385 36 64 95 125 156 186 217 248 278 309 3396 37 65 96 126 157 187 218 249 279 310 3407 38 66 97 127 158 188 219 250 280 311 3418 39 67 98 128 159 189 220 251 281 312 3429 40 68 99 129 160 190 221 252 282 313 34310 41 69 100 130 161 191 222 253 283 314 34411 42 70 101 131 162 192 223 254 284 315 34512 43 71 102 132 163 193 224 255 285 316 34613 44 72 103 133 164 194 225 256 286 317 34714 45 73 104 134 165 195 226 257 287 318 34815 46 74 105 135 166 196 227 258 288 319 34916 47 75 106 136 167 197 228 259 289 320 35017 48 76 107 137 168 198 229 260 290 321 35118 49 77 108 138 169 199 230 261 291 322 35219 50 78 109 139 170 200 231 262 292 323 35320 51 79 110 140 171 201 232 263 293 324 35421 52 80 111 141 172 202 233 264 294 325 35522 53 81 112 142 173 203 234 265 295 326 35623 82 113 143 174 204 235 266 296 327 35724 55 83 114 144 175 205 236 267 297 328 35825 56 84 115 145 176 206 237 268 298 329 35926 57 85 116 146 177 207 238 269 299 330 36027 58 86 117 147 178 208 239 270 300 331 36128 59 87 118 148 179 209 240 271 301 332 36229 88 119 149 180 210 241 272 302 333 36330 89 120 150 181 211 242 273 303 334 36431 90 151 212 243 304 365

12345678910111213141516171819202122232425262728293031

54 6

365334

Jan 6

= 37 Days= 37 Days

Method 2.Method 2.Nov 30

Dec 31

= 31 Days= 31 Days


6 - 21Simple

Interest

Simple

Interest 66 66

01.0603


i


2nd

CPT

Enter

Method 3.Method 3.



earned on $5000

invested from

Nov. 30th,, 02 to Jan

6th. 03 at 4.5%.

Start

DBD = 37 Date

11.3002 Enter


6 - 22Simple

Interest

Simple

Interest 66 66


I =$5000*.045 * 37/365

I = $22.81I = $22.81


at 4.5%

for ? .

37 Days


6 - 23Simple

Interest

Simple

Interest 66 66

Method 1.Method 1.

What is the interest earned on $5000 invested from Oct 11th , 02 to Mar

11th, 03 at 4.0%?

Oct 11th to end of month = 20Days

Total = 61 Total = 59

151 151

Jan & Feb

Mar To 11th of month = 11

Nov & Dec30 31

2831

Includes the last date



6 - 24Simple

Interest

Simple



1 32 60 91 121 152 182 213 244 274 305 3352 33 61 92 122 153 183 214 245 275 306 3363 34 62 93 123 154 184 215 246 276 307 3374 35 63 94 124 155 185 216 247 277 308 3385 36 64 95 125 156 186 217 248 278 309 3396 37 65 96 126 157 187 218 249 279 310 3407 38 66 97 127 158 188 219 250 280 311 3418 39 67 98 128 159 189 220 251 281 312 3429 40 68 99 129 160 190 221 252 282 313 34310 41 69 100 130 161 191 222 253 283 314 34411 42 70 101 131 162 192 223 254 284 315 34512 43 71 102 132 163 193 224 255 285 316 34613 44 72 103 133 164 194 225 256 286 317 34714 45 73 104 134 165 195 226 257 287 318 34815 46 74 105 135 166 196 227 258 288 319 34916 47 75 106 136 167 197 228 259 289 320 35017 48 76 107 137 168 198 229 260 290 321 35118 49 77 108 138 169 199 230 261 291 322 35219 50 78 109 139 170 200 231 262 292 323 35320 51 79 110 140 171 201 232 263 293 324 35421 52 80 111 141 172 202 233 264 294 325 35522 53 81 112 142 173 203 234 265 295 326 35623 82 113 143 174 204 235 266 296 327 35724 55 83 114 144 175 205 236 267 297 328 35825 56 84 115 145 176 206 237 268 298 329 35926 57 85 116 146 177 207 238 269 299 330 36027 58 86 117 147 178 208 239 270 300 331 36128 59 87 118 148 179 209 240 271 301 332 36229 88 119 149 180 210 241 272 302 333 36330 89 120 150 181 211 242 273 303 334 36431 90 151 212 243 304 365

12345678910111213141516171819202122232425262728293031

54

Oct 11Dec 31 365

284 = 81 Days= 81 Days

Mar 11 70 = 70 Days= 70 Days

=151 Days=151 Days

Method 2.Method 2.


6 - 25Simple

Interest

Simple

Interest 66 66

03.1103


i


2nd

CPT

Enter

Method 3.Method 3.



earned on $5000

invested from

Oct. 11th,, 02 to Mar

11th. 03 at 4.0%.

Start

DBD = 151 Date

10.1102 Enter


6 - 26Simple

Interest

Simple

Interest 66 66


I =$5000* .04 * 151/365

I = $82.74I = $82.74


at 4.0%

for ? .

151 Days


6 - 27Simple

Interest

Simple

Interest 66 66


We can ‘reorganize’ the formula to also get each of the following separately:

PrincipalRateRateTimeTime

Shortcut Tool!Shortcut Tool!


6 - 28Simple

Interest

Simple

Interest 66 66

IPrt

Formula Formula I = PrtTo help remember this…

we can place the formula into a triangle as follows…

The Triangle …another useful non-calculator!

Where variables are BESIDE EACH OTHER this

means to MULTIPLY!

Using this tool!Using this tool!

P*r*tP*r*t

IPrt

Where a variable is ABOVE ANOTHER this means to

DIVIDE!


6 - 29Simple

Interest

Simple

Interest 66 66

If you want to find P then I /rt

If you want to find r

then I /Pr

then I /Pt

If you want to find t


IPrt

The Triangle …another useful non-calculator!


6 - 30Simple

Interest

Simple

Interest 66 66

What is a Time Line?

A Time Line is, as the name suggests, a line that shows the various points of time along

which a loan or investment travels to maturity.

It is used for diagramming problems involving multiple payments or investments.

Two BenefitsTwo Benefits…Helps organize data…Helps organize data

…Indicates the steps needed to implement the solution

…Indicates the steps needed to implement the solution

Using a Time LineTime Line


6 - 31Simple

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Simple

Interest 66 66

Calculate the interest earned at 4% on $5000 invested from Oct. 11th to March 11th

Calculate the interest earned at 4% on $5000 invested from Oct. 11th to March 11th

Draw a line for the entire period

Step 1Step 1

Oct 11 March 11

$5000

Start Finish

Enter the key dates on the line

Step 2Step 2Dec 31

Enter the number of days

between each date and

add

Step 4Step 4

81 days70 days

151 days

Enter the Investment

Step 3Step 3

The calculation can now be restated as follows…

284 365 70

Look up



6 - 32Simple

Interest

Simple

Interest 66 66

Calculate the interest earned at 4% on $5000 invested for 151 days.

Calculate the interest earned at 4% on $5000 invested for 151 days.

I = 5000 *


IPrt = $82.74

I = Prt

.04 * 151/365



6 - 33Simple

Interest

Simple

Interest 66 66 You can now use this tool!You can now use this tool!

IPrt

In the next few examples you have to…(a) First identify which variable you are being asked to solve for, and

In the next few examples you have to…(a) First identify which variable you are being asked to solve for, and

(b) Reorganize the formula in order to meet the requirement in (a).

(b) Reorganize the formula in order to meet the requirement in (a).


6 - 34Simple

Interest

Simple

Interest 66 66 Calculating the

PrincipalPrincipal

Formula Formula I rtP=

P = $195 .0525 *(150/365)

P = $195

P = $9,038.10

.0121575342

$195 interest is earned on a 150 day GIC at 5.25%.

Find the initial investment .


6 - 35Simple

Interest

Simple

Interest 66 66

.0525

*150/

365=/

195

=

$9038.10$9038.101/x1/x

9038.10

P = $195 .0525 *(150/365)


6 - 36Simple

Interest

Simple

Interest 66 66 Calculating the RateCalculating the Rate

What Rate of Interest is needed to earn $200 on a

$5000 investment invested for 180 days?

What Rate of Interest is needed to earn $200 on a

$5000 investment invested for 180 days?

r =

Formula Formula r = I Pt

/($5000*180/365)$200

$200

0.081111 or 8.11% /2465.75 r =

r =


6 - 37Simple

Interest

Simple

Interest 66 66

5000

*180/

365=/

200

=

8.11%8.11%1/x1/x

0.08111

/($5000*180/365) r = $200


6 - 38Simple

Interest

Simple

Interest 66 66 Calculating the TimeCalculating the Time

What is the length of Time required for $2000 to grow to

$2100 when invested at 5.6%?

What is the length of Time required for $2000 to grow to

$2100 when invested at 5.6%?

Formula Formula t I P= r

Step 1Step 1 Find the amount of InterestFind the amount of Interest

$2100

PP

= $100

More

- $2000

IIP + I = SumP + I = SumI


6 - 39Simple

Interest

Simple

Interest 66 66

What is the length of Time required for $2000 to grow to $2100 when invested at 5.6%?

What is the length of Time required for $2000 to grow to $2100 when invested at 5.6%?

t = / ($2000*.056)/ ($2000*.056)t =

$100$100/ 112

t = 0.8928 Years

t = 326 days

Step 2Calculate

Step 2Calculate

Calculating the TimeCalculating the Time

Formula Formula t I P= r

*365 days*365 days


6 - 40Simple

Interest

Simple

Interest 66 66

100

2000/

0.056=

365=

326 days326 days

325.89

/ ($2000*.056)/ ($2000*.056)$100t =

/

0.8928 Years*


6 - 41Simple

Interest

Simple

Interest 66 66


6 - 42Simple

Interest

Simple

Interest 66 66


P + ISum =

Up to this point we have used two formulae:

Now, we substitute for INow, we substitute for I

withwith PrtStep 1Step 1

P +Sum =

Collecting like termsCollecting like terms

Formula Future ValueFuture Value Sum =P(1+rt)

Step 2Step 2

& Sum = P + IWe can combine them as follows:


6 - 43Simple

Interest

Simple

Interest 66 66

Sum = P(1+rt)

I place $17000 in a 150 day

term deposit on Jan. 6 paying

6.5%.

I place $17000 in a 150 day

term deposit on Jan. 6 paying

6.5%.How much will the bank pay me on the

maturity date?

How much will the bank pay me on the

maturity date?

S = $17454.11

S = $17000(1.0267123)

S = $17000 1+ .065(150)365


6 - 44Simple

Interest

Simple

Interest 66 66

.065

Date of Maturity

*150/

365=+1=

$17454.11$17454.11

*17000

S = $17000 1+ .065(150)365

17454.11

=


6 - 45Simple

Interest

Simple

Interest 66 66

Day of Month


1 32 60 91 121 152 182 213 244 274 305 3352 33 61 92 122 153 183 214 245 275 306 3363 34 62 93 123 154 184 215 246 276 307 3374 35 63 94 124 155 185 216 247 277 308 3385 36 64 95 125 156 186 217 248 278 309 3396 37 65 96 126 157 187 218 249 279 310 3407 38 66 97 127 158 188 219 250 280 311 341

1234567

Determine the Maturity DateDetermine the Maturity Date

I place $17000 in a 150 day term deposit on Jan. 6 paying 6.5% pa.I place $17000 in a 150 day term deposit on Jan. 6 paying 6.5% pa.

= 6 days +150 = 156 days

Find 156

Find 156 The Term Deposit will mature on June 5th.

Look up


6 - 46Simple

Interest

Simple

Interest 66 66

5,000

8,000

10,000

During the year, I invested the following funds at a constant 4% p.a.

Feb 14th $5,000

Mar 17th $3,000

July 1st $2,000

What Total amount will I have on December 29th?What Total amount will I have on December 29th?

(The second and third amounts were added to the Feb 14th amount.)


6 - 47Simple

Interest

Simple

Interest 66 66

Step 1

Three Steps are required to solve this problem:

Draw a time line, including the dates and dollar amounts.

Step 2

Determine the time between each of the

dates

Step 3

Calculate the interest amounts,

and add together.


6 - 48Simple

Interest

Simple

Interest 66 66

Step 1

Draw a time line

Feb 14 March 17 July 1 Dec 29

45 76 182 363

$5000

$3000

$2000

363 – 45 = 318 Days

363 – 76 = 287 DaysStep 2

Determine the Time

363 – 182 = 181 Days

Look up


6 - 49Simple

Interest

Simple

Interest 66 66

S = $10308.28Total Amount

S = $10308.28Total Amount

Step 3

Calculate the

Interest amounts, and

add togethe

r.

Calculate the

Interest amounts, and

add togethe

r.


I1 = 5000 *.04 *318/365 $174.25

I2 = 3000 *.04 *287/365

I3 = 2000 *.04 *182/365

94.36

39.67

$308.28

$10000 +$10000 + $308.28

$308.28


6 - 50Simple

Interest

Simple

Interest 66 66

“During the year I made an investment that had changes in

the rate of interest.How do I determine the total

interest earned during the period under review?”

Every time the interest rate changes,you must stop and

make a calculation up to that point.


6 - 51Simple

Interest

Simple

Interest 66 66

I invest $1,000 on Feb. 14th at 6%.The changes in interest rates to July 4th

are as follows:

Investment Date rate

$1,000 Feb 14th 6%

April 20th 6.8%

May 18th 7.1%

How much Interest did I earn up to July 4th ?How much Interest did I earn up to July 4th ?


6 - 52Simple

Interest

Simple

Interest 66 66

Look up

for Days

… by finding the number of days between each rate change!

Investment Date rate

$1,000 Feb 14th 6%

April 20th 6.8%

May 18th 7.1%

July 4th


6 - 53Simple

Interest

Simple

Interest 66 66

= 45= 110 = 65 Days

= 28 Days

Number of Days

Number of Days

Table reading

Table reading

Look up

for Days

Feb 14th

April 20th

May 18th

July 4th = 47 Days

Interest EarnedInterest Earned

= 138

= 185


6 - 54Simple

Interest

Simple

Interest 66 66

Feb 14th

April 20th65 Days


I1 = 1000 * .06 * 65/365 = $10.68

May 18th

28 DaysI2 = 1000 * .068 * 28/365

I3 = 1000 * .071 * 47/365

= 5.22

July 4th47 Days

= 9.14

$25.04$25.04

Interest EarnedInterest Earned


6 - 55Simple

Interest

Simple

Interest 66 66


6 - 56Simple

Interest

Simple

Interest 66 66

What are we being asked to provide?

“How much must I invest…

to grow…”

“How much must I invest…

to grow…”

…this suggests finding the

Principal

How much must I invest in order for it to grow to $5000 within 6 months @ 4.4% simple interest?


6 - 57Simple

Interest

Simple

Interest 66 66

What data do we need?

We need the appropriate data to be

able to use the appropriate formula…We need the appropriate data to be

able to use the appropriate formula…

Formulae Formulae I = Prt & Sum = P(1+rt)

How much must I invest in order for it to grow to $5000 within 6 months, @ 4.4% simple interest?



6 - 58Simple

Interest

Simple

Interest 66 66

r = 4.4% t = 6 months = .5Sum = $5000



What data do we have?



6 - 59Simple

Interest

Simple

Interest 66 66

As we know the Sum, the formula now becomes…




Using Sum = P(1+rt)

P = Sum/(1+rt)


6 - 60Simple

Interest

Simple

Interest 66 66

P =5000/ 1 + 0.044(.5)

P = $4892.37P = $4892.37



FormulaFormula P = Sum/(1+rt)


6 - 61Simple

Interest

Simple

Interest 66 66

LO-2LO-2

Simple

Interest

Simple

Interest 66 66


6 - 62Simple

Interest

Simple

Interest 66 66

Future

Value

What is the equivalent value on September 15 of a $2000 payment on July

4, if money is worth 6% pa?

What is the equivalent value on September 15 of a $2000 payment on July

4, if money is worth 6% pa?

Step 1

Step 2

Draw a Timeline

July 4 September 15

$2000

2000[1+.06(69/365)]

= $2022.68= $2022.68

Sum =

69 Days

Sum = P(1+rt)


6 - 63Simple

Interest

Simple

Interest 66 66

Present Value

What is the equivalent value on May 18th of a $2000 payment due on the following December 15th if money can earn 5.2%?

What is the equivalent value on May 18th of a $2000 payment due on the following December 15th if money can earn 5.2%?

Step 1

Step 2

Draw a Timeline

May 18 December 15

$2000

= 2000/[1+.052(211/365)]

211 Days

= $1941.63= $1941.63

P = Sum/(1+rt)


6 - 64Simple

Interest

Simple

Interest 66 66

Heather owes Mark $3000 payable on April 27.

If money can earn 4%, what amount should Mark accept in

settlement of the debt:A) 30 days before the scheduled

payment?B) 90 days before the scheduled

payment?


6 - 65Simple

Interest

Simple

Interest 66 66

Step 1

Draw a Timeline

April 27

Present Value30 days

90 days

$3000

Step 2 P = Sum/(1+rt)


6 - 66Simple

Interest

Simple

Interest 66 66

AA P = 3000/[1+.04(30/365)]

P = $2990.17P = $2990.17

BB P = 3000/[1+.04(90/365)]

P = $2970.17P = $2970.17

P = Sum/(1+rt)


6 - 67Simple

Interest

Simple

Interest 66 66

You can prepay $1234 tuition for a course or delay payment for 3 months and pay

$1432.

If you can earn 6% on your money, which option should you choose?


6 - 68Simple

Interest

Simple

Interest 66 66

Data

$1234 = Present Value = P1

$1432 = Future Value = S2

P2 = 1432/[1+.06(.25)]

Tip:Find the PV of the

future payment!

Tip:Find the PV of the

future payment! P2 = $1410.84

Money saved ($176.84) by paying now!

Which formula should

you use?

Which formula should

you use? $1234.00

P = Sum/(1+rt)P = Sum/(1+rt)3

months = 1/4

3 months = 1/4


6 - 69Simple

Interest

Simple

Interest 66 66

This completes Chapter 6This completes Chapter 6

Business Mathematics Jerome Chapter 06

Education

Transcript of Business Mathematics Jerome Chapter 06