Question

Suppose you deposit $2,688.00 into an account today. In 14.00 years the account is worth $3,748.00. The account earned ____% per year.

Today is Derek’s 25th birthday. Derek has been advised that he needs to have $2,656,763.00 in his retirement account the day he turns 65. He estimates his retirement account will pay 10.00% interest. Assume he chooses not to deposit anything today. Rather he chooses to make annual deposits into the retirement account starting on his 28.00th birthday and ending on his 65th birthday. How much must those deposits be?

Answer 1

1.Information provided:

Future value= $3,748

Present value= $2,688

Time= 14 years

The question is solved by calculating the yield to maturity.

The yield to maturity is calculated by entering the below in a financial calculator:

FV= 3,748

PV= -2,688

N= 14

Press the CPT key and I/Y to compute the yield to maturity.

The value obtained is 2.4029.

Therefore, the account earned 2.40% per year.

2.Information provided:

Future value= $2,656,763

Time= 65 years - 28 years = 37 years

Yield to maturity= 10%

Enter the below in a financial calculator to compute the amount of annual deposit:

FV= 2,656,763

N= 37

I/Y= 10

Press the CPT key and PMT to compute the amount of annual deposit.

The value obtained is 8,049.83.

Hence, Derek must deposit $8,049.83 every year to have $2,656,763.