After graduation,you plan to work for Dynamo Corporation for 12 years and then start your own business.You expect to save and deposit $7,500 a year for the first 6 years (t = 1 through t = 6)and $15,000 annually for the following 6 years (t = 7 through t = 12).The first deposit will be made a year from today.In addition,your grandfather just gave you a $32,500 graduation gift which you will deposit immediately (t = 0).If the account earns 9% compounded annually,how much will you have when you start your business 12 years from now?

Question

Quizplus · Accepted Answer

To solve this problem, we can use the formula for the future value of an annuity:

FV = PMT * [(1 + r)^n - 1]/r

where PMT is the annual deposit amount, r is the annual interest rate, and n is the number of periods.

For the first 6 years, PMT = $7,500 and n = 6. So the future value of these deposits at the end of year 6 is:

FV1 = $7,500 * [(1 + 0.09)^6 - 1]/0.09 = $58,054.20

For the following 6 years, PMT = $15,000 and n = 6. So the future value of these deposits at the end of year 12 is:

FV2 = $15,000 * [(1 + 0.09)^6 - 1]/0.09 = $123,642.33

Finally, we need to calculate the future value of the $32,500 gift at the end of year 12. We can simply use the compound interest formula:

FV3 = $32,500 * (1 + 0.09)^12 = $101,195.17

The total future value of all three amounts is:

FV1 + FV2 + FV3 = $58,054.20 + $123,642.33 + $101,195.17 = $282,891.70

So the answer is C) $298,892.

After Graduation,you Plan to Work for Dynamo Corporation for 12