Question

1) Alice pays $200 at the end of each month for 10 years into a fund paying 8% per month compounded monthly.

a) What is the value of the fund at the end of the 10th year?

b) At the end of the 10th year, the payments cease, but the balance continues to earn interest. What is the value of the fund at the end of the 20th year?

c) After the 20 years, Alice will make withdraws each month. How much can she draw out of the fund at the end of each month so that the fund will be empty after 15 years?

Answer 1

1) a) PMT = 200, n = 10*12 = 120, r = 8% per month

Hence the amount after 10 years = $36589.21

b) n = 120, P = 36589.21, A = ?

Hence at the end of 20th year the amount will be $81214.88.

c) Now it's like a loan of $81214.88 and bank is giving interest of 8% on it and paying a monthly payment for next 15 years.

PV = 81214.88, r = 0.08, n = 12, t = 15, nt=12*15 = 180

So, she can withdraw $776.13 each month for next 15 years.

Please comment if any doubt. Thank you.