Your grandfather put some money into an account for you on the day you were born. You are now 18 years old and are allowed to withdraw the money. The account currently has $ 4 comma 057 in it and pays an interest rate of 6 %. a. How much money would be in the account if you left the money there until your 25th birthday? b. What if you left the money until your 65th birthday? c. How much money did your grandfather originally put into the account?

a) $6,100

b) $62,742

c) $1,421

Explanation:

a. How much money would be in the account if you left the money there until your 25th birthday?

To find the answer, we use the future value formula:

FV = PV (1 + i) ^n

Where:

FV = Future Value PV = Present Value i = interest rate n = number of compounding periods

Because the difference from your 18th birthday to your 25th birthday is 7 years, the number of compounding periods is 7. Now we can plug the amounts into the formula:

FV = $4,057 (1 + 0.06) ^7

FV = $6,100

b. What if you left the money until your 65th birthday?

We use the future value formula again. Our present value will be the $6,100 that the account has by your 25th birthday. Because the difference between 65 and 25 is 40, the number of compounding periods is 40 as well.

FV = $6,100 (1 + 0.06) ^40

FV = $67,742

c. How much money did your grandfather originally put into the account?

To find this answer, we use the present value formula:

PV = FV (1 + i) ^-n

(the symbols represent the same as in the future value formula)

Now, we simply plug the amounts into the formula:

PV = $4,057 (1 + 0.06) ^-18

PV = $1,421