Question

Adam is turning 40 years old today and plans to retire on his 65th birthday. He starts making annual deposits ( starting on the day of his 40th birthday) into an account that pays 15% compunded quarterly. He plans to withdraw $10,000 quarterly from the account starting on his 65th birthday unitil his 75th birthday (inclusive). Note that the lst deposit is made at the same time as the first withdrawal.

what is the effective interest rate for deposits?

WHat is the present worth (now) of withdrawals?

WHat is the amount of the deposits

Answer 1

A. Effective interest rate per quarter = 0.15/4 = 0.0375

Effective interest rate = 3.75% per quarter.

Annula Effective rate of interest can be calculated using the following formula

Effective rate of interest = 15.87% per year

B. Withdrawal plan = $ 10,000

Starting from the 65th birthday and till 75th year(inclusive). Therefore total payment = 41 quarters of $ 10,000 per quarter.

Present value of this withdrawal today can be calculated as follows

C. Let us assume the deposit is A.

Amount of deposit can be calculated as follows

Amount of deposit = 215,509.90 (A/F,15.87%,26)

Amount = 215,509.90 × 0.003525547

Amount = $ 760 (Approximately).

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