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Answers

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Compound Interest

Compounding interest is where money earned is added to the principal and then recalculated to find a new amount.

Movie Clip

http://www.youtube.com/watch?v=Uka5owZdFDI&feature=related

Compound Interest

p = principal (the amount you start with – for example the amount you invest, the amount you take the loan for etc…)

r = rate (it’s the % - but change it to a decimal for this formula

t = time in years

n = # of times it’s compounded per year

(1 )ntr

A Pn

Example1:

John earns 6% annual interest compounded annually (or 1 time per year) on his $1000 investment. How much money will John have after 4 years?

In the first year John will earn:

11000(1 .06)A

$1060.00ANow take the new amount and put it into the principal to find the amount he will have in the second year.

11060.00(1 .06)A

$1123.60ANow take this amount and use it as the new principal to find the balance in the third year. This process is what we call recursive (using the previous answer to help us find the next.)

The balance after the 4th year is calculated using $1191.02 as the principal.

$1191.02A

11123.60(1 .06)A

11191.02(1 .06)A

$1262.48A

How much would you earn on this investment after 4 years?

$1262.48 – $1000.00 = $262.48

Remember*If it compounds semi-annual n = 2

If it compounds quarterly n = 4

If it compounds monthly n = 12

Example 2:How much money will you have at age 18yrs. if your parents invest $12,000 at 10% compounded annually for 2 years?

2(1).1012000(1 )

1A

In 2 years you will have $14,520 in that account.

(1 )ntr

A Pn

Example 3:If you invest $25.00 at 6% interest compounded semi-annually, how much will you have after 1 year?

You would have $26.52 in your account.

(1 )ntr

A Pn

2 1

.0625.00 1

2A

You Try: If you invest $1,000 at 8% interest compounded semi-annually how much will you have after 1 year?

(1 )ntr

A Pn

How much would you have after 1 years at this rate?

Answer: $1,081.60

Find Principle when the Accumulated Savings are given:

Tony is saving for a new ipod nano, it costs $150. He wants to buy it in 2 years. How much does he need to put in a savings account now to get $150 at the end of 2 years. The account earns 5% interest, compounded annually.

Find Principle when the Accumulated Savings are given:

Tony is saving for a new ipod nano, it costs $150. He wants to buy it in 2 years. How much does he need to put in a savings account now to get $150 at the end of 2 years. The account earns 5% interest, compounded annually.

(2)(1)

2

(1 )

.05150 (1 )

1

150 (1.05)

150 (1.1025)

150

1.1025

$136.05

ntrA P

n

P

p

p

p

How much money should I save in an account paying 10% interest compounded yearly if I want to have $2420 in 2 years?

How much money should I save in an account paying 10% interest compounded yearly if I want to have $2420 in 2 years?

(2)(1)

2

(1 )

.102420 (1 )

12420 (1.10)

2420 (1.21)

24201.21

$2000

ntrA P

n

P

p

p

p

You TryA necklace is appraised at $2880. If the value of

the necklace has increased at an annual rate of 20%, how much was it worth 2 years ago?

You TryA necklace is appraised at $2880. If the value of

the necklace has increased at an annual rate of 20%, how much was it worth 2 years ago?

$ 2000

If a house is valued at $103,500. If it’s value has increased at an annual rate of 15%, how much was it worth 1 year ago?

If a house is valued at $103,500. If it’s value has increased at an annual rate of 15%, how much was it worth 1 year ago?

$90,000

Homework 10.5

Summary: Name three ways compound interest may affect you in the future?