The Mathematics of Money

Whichever way we arrive at the number of doublings, we can fi nish the problem by noting

that since the time allowed is 30 years, the money would need to double approximately every

30/5 
 6 years. Then 72/6 
 12, and so we conclude that the interest rate would need to

be approximately 12%.

It is important to remember though that this is only a rough approximation. You can see for

yourself just how close it is by using this interest rate with the $30,000 for 30 years to see

how close the future value is to the desired $1,000,000. You can improve on the approxi-

mation by finding the future value and tweaking our 12% estimate. If 12% gives a value

that is too high, try a rate that is a bit lower. If 12% gives a too low future value, try using

a rate that is a bit higher. Improving on the Rule of 72 estimate in this way requires a bit of

trial and error, but it does allow us to come up with a more precise value if we need it.

A. Basics of Compound Interest

1. Suppose that you deposit $2,500 in an account paying 7% interest that compounds annually for 4 years. Fill in the
   missing values in the table below, which shows how your account value would grow:

Year Start of Year Interest End of Year

1 $2,500.00

2

3

4

2. If the account from Exercise 1 had paid simple interest, how much less would you have had at the end of the
   4 years?


3. Suppose that you deposit $4,250 in an account that pays 6½% annually compounded interest for 5 years. Set up
   a table similar to the one used in Exercise 1 and use it to show the growth in this account’s value over the course of its
   5-year term.

B. Using the Compound Interest Formula for FV

Be sure to read each question carefully to determine whether it is asking for the future value or the total interest.

4. If I invest $25,112 at 7.24% annually compounded interest for 25 years, how much will I end up with?


5. Tris deposited $3,275.14 into a 5-year credit union certifi cate of deposit paying 5.13% interest compounded annually.
   How much will his CD be worth at maturity?

EXERCISES 3.1

Exercises 3.1 97

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