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 $37,500 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?
A) $372,417
B) $309,826
C) $312,955
D) $359,899
E) $334,862

Question

Quizplus · Accepted Answer

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

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

where FV is the future value, PMT is the annual payment, r is the interest rate, and n is the number of years.

First, let's calculate the future value of the deposits. For the first 6 years, the PMT is $7,500 and n is 6. The interest rate is 9%, compounded annually. Plugging these values into the formula, we get:

FV1 = 7,500 x [(1 + 0.09)^6 - 1] / 0.09 = $63,278.46

For the next 6 years, the PMT is $15,000 and n is 6. Using the same formula, we get:

FV2 = 15,000 x [(1 + 0.09)^6 - 1] / 0.09 = $136,676.46

Now, let's calculate the future value of the graduation gift. The present value is $37,500, and we will compound it for 12 years at an interest rate of 9%. Using the formula for the future value of a lump sum, we get:

FV3 = 37,500 x (1 + 0.09)^12 = $122,000.23

Finally, we add up the three future values to get the total:

FV = FV1 + FV2 + FV3 = $63,278.46 + $136,676.46 + $122,000.23 = $322,955.15

Therefore, the answer is C) $312,955.

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