Question

Question 10 (3 points)

4) Listen
A father is planning a savings program to put his daughter through college. His
daughter is now 13 years old and he anticipates that he needs to save $ 62,649 for
tuition, books and board when his daughter begins college. The daughter recently
received $9,902 from her grandfather's estate which will also be used to help meet
the cost of her education. Assume the father wishes to make 5 equal deposits to a
money market account paying 8 percent interest compounded annually. He will make
his first deposit one year from today and his last deposit the day she starts college.
What will his annual deposits be?

Answer 1

To find the annual deposits the father needs to make, we can use the formula for the future value of an ordinary annuity:

Future Value = Payment * [(1 + Interest Rate)^Time - 1] / Interest Rate

Where:
- Future Value is the desired amount ($62,649)
- Payment is the annual deposit
- Interest Rate is the annual interest rate (8% or 0.08)
- Time is the number of years (13 years)

Using the given information, we have:

Future Value = $62,649
Interest Rate = 0.08
Time = 13 years

Now we can rearrange the formula to solve for Payment:

Payment = Future Value * (Interest Rate / [(1 + Interest Rate)^Time - 1])

Payment = $62,649 * (0.08 / [(1 + 0.08)^13 - 1])

Calculating this, the father needs to make annual deposits of approximately $4,393.25 in order to accumulate $62,649 over a period of 13 years, considering an 8% annual interest rate compounded annually.