Question

Yumi's grandparents presented her with a gift of $22,000 when she was 9 years old to be used for her college education. Over the next 8 years, until she turned 17, Yumi's parents had invested her money in a tax-free account that had yielded interest at the rate of 4.5%/year compounded monthly. Upon turning 17, Yumi now plans to withdraw her funds in equal annual installments over the next 4 years, starting at age 18. If the college fund is expected to earn interest at the rate of 5%/year, compounded annually, what will be the size of each installment? (Assume no interest is accrued from the point she turns 17 until she makes the first withdrawal. Round your answer to the nearest cent.)

Answer 1

Information provided:

Present value= $22,000

Time= 8 years*12 = 96 months

Interest rate= 4.5%/12 = 0.3750% per month

The question is solved by first calculating the future value at the end of 17 years.

Enter the below in a financial calculator to compute the future value of ordinary annuity:

PV= -22,000

N= 96

I/Y= 0.3750

Press the CPT key and FV to compute the future value.

The value obtained is 31,512.02.

Therefore, the gift will accumulate to $31,512.02 at age 18.

Information provided:

Present value= $31,512.02

Time= 4 years

Interest rate= 5%

The amount of installment is calculated by entering the below in a financial calculator:

PV= -31,512.02

N= 4

I/Y= 5

Press the CPT key and PMT to compute the amount of installment.

The value obtained is 8,886.76.

Therefore, the size of each installment is $8,886.76.

In case of any query, kindly comment on the solution.