Quiz 3         MAT 118, Spring 2003

1. You will need $2400 in cash two years from now. Your parents tell you that if you give them some amount of money now, they will pay you 10% annual simple interest on it, with no compounding. How much money do you need to give them in order to have the$2400 in two years?

Solution: First, we recall that for simple interest, . In our case, we know the future value is $2400, that the annual rate is 10%, and the time is 2 years. We want to know the principle . Since both the rate and the time are given in years, all our units match and there is no need for conversion. Thus, we need to solve for , giving So we need to give them$2000 now to have $2400 in two years. 2. If you invest$1000 in a bank account that pays 8% annual interest, compounded monthly, how much will there be in the account after 3 years?

Solution: Our principle is $1000. Since the account is compounded monthly, our periodic interest rate is (there are 12 months in a year). We also need to express our time in months, and 3 years is 36 months. Thus, the amount is expressed as 3. If you invest$1000 at 8% annually, compounded monthly, how many months will it be until you double your money?

Solution: Since we want to double our money, the future value should be $2000. As above, the periodic rate is , the principle is$1000, and the time is in months. Thus, we need to solve

for . First, divide both sides by 1000 to get

and then take the logarithm of both sides. Using the fact that , we get

Now divide to get

This is 104.31 months, that is, just over 8 years and 8 months.

(Note that on the original quiz, the correct answer had a typo, so everyone got full credit on this problem, no matter which choice they picked. Duh.)

Scott Sutherland 2003-02-14