Question

On your birthday, when you turned 20, $12100 was deposited in an account which earns 10.5% compounded annually. a. How much can you withdraw annually for 16 years if the first withdrawal is made on the day you become 45? $ b. State the total amount of interest earned on this account. $

Answer 1

a)

Future value = Present value *(1+r)^n

where , r = interest rate

n = number of periods

Balance at the age of 45 = 12,100*(1+10.50%)^25 = $146,839.31

Present value of annuity due = P*[1 - (1+r)^-n / r ]*(1+r)

where, P = annual withdrawls

r = interest rate

n = number of periods

146,839.31 = P*[1 - (1+10.50%)^-16 / 10.50% ]*(1+10.50%)

P = 17,493.73

Anual withdrawls = $17,493.73

b)

Total interest :

interest for the first 25 years = 146,839.31 - 12100 = 134739.31

interest for the next 16 periods = (16*17,493.73) - 146839.31 = 133,060.38

Total interest = 134739.31 + 133,060.38 = $267,800 (rounded to nearest dollar)