Applied Math 40S April 30, 2008

or fade away

Watching It Grow ...

Foreign Currency and Coins by flickr user bradipo

Solve for N (the number of payments) ...

To buy a new car you must take out a loan of $10 593.30. You can afford a payment of $238 per month. The dealership offers you an annual interest rate of 3.75% compounded monthly.

How many payments must you make?

How much interest have you paid?N=I%=PV=PMT=FV=P/Y=C/Y=PMT: END BEGIN

48

What's the difference?

N=I%=PV=PMT=FV=P/Y=C/Y=PMT: END BEGIN


Solve for I (the rate of interest) ...

A certain university program will cost $20 000. What annual interest rate, compounded monthly, must you obtain if you can save $288.50 per month for the next five years and hope to have all the money saved by that time?

Solve for PV (the value now) ...

You plan to buy a car. You can make monthly payments of $525 and the interest rate advertised for car loans is 6.25%, compounded monthly. If the dealership is offering you financing for two years how much car can you afford?

Solve for FV (the future value) ...

You decide to invest $6500. The bank offers an interest rate of 8.25% compounded annually. What will your money be worth in 7 years if the interest rate remains unchanged?

Watching Money Grow ...

Calculate the final balance if $7500 were invested at 8% per year, compounded semi-annually for 6 years.

How long will it take $12 000 invested at 7.2% per year, compounded quarterly, to grow to $15 000?



Investing Regularly ...Calculate the final balance if $1500 were invested at 8% per year, compounded semi-annually, with additional investments of $1 000 at the end of every six months for five years.

How long will it take to save $35 000, if $2 500 were invested at 7.2% per year, compounded quarterly, followed by an additional $400 at the end of each 3-month period?



Investing Frequently ...A financial institution offers an annual interest rate of 6%, compounded monthly.Compare $1200 invested at the end of each year to $100 invested at the end of each month.

Option 1: $1200/year Option 2: $100/month

Here's a handy way to figure out how long your investment will take to double in value. It is called the Rule of 72.

(Interest Rate %) x (Years to Double) = 72

To find the number of years given a percentage:

To find the percentage required to double given the years:

The Rule of 72

Years = 72(Interest Rate %)

Rate = 72Years

Numbers 72 by flickr user szczel

Scenario 2: You are shopping for an investment that will double in 6 years. What interest rate are you looking for?

Scenario 1: You have an investment that compounds annually at 7%. How long will it take to double?

Use the Rule of 72 to estimate the doubling time for these interest rates:

(a) 4% per annum, compounded annually

(b) 8% per annum, compounded annually

(c) 24% per annum, compounded annually

Use the TVM solver in your calculator to calculate the the compound amount of a $100 investment for the doubling times estimated above.

How accurate does the Rule of 72 seem to be?




HOMEWORK

Shaina wishes to invest $2000 given by her grandfather. She has an option of a guaranteed investment certificate earning 8.75%, compounded quarterly, or a savings bond of 9%, compounded semi-annually.

Which investment should she choose?

If each investment term is 5 years, what will be the difference in their values at the end of the term?

HOMEWORK

Suppose an uncle has left you $100 000 to invest, on condition that you give one-half of all interest earned to the SPCA. You decide to invest it in a savings account that pays 5% interest compounded quarterly. How much will you have given to the animal shelter after:

one month? 3 months?N=I%=PV=PMT=FV=P/Y=C/Y=PMT: END BEGIN




10 years?2 months?

HOMEWORK

Applied Math 40S April 30, 2008

Education

Transcript of Applied Math 40S April 30, 2008