Question

Mr. Ford deposited $ 100,000 dollars in a bank, stipulating that after 10 years he would begin to pay him or his heirs $ 4,000 dollars monthly overdue. For how many months will Mr. Ford receive this rent? The bank pays 8.5% per annum capitalizable every month. If the result is not exact, calculated the value of the last payment.

Answer 1

Initial Deposit = $ 100000, Interest Rate = 8.5 % capitalizable (compounded) every month, Applicable Monthly Rate = (8.5/12) = 0.7083 % , Deposit Tenure = 10 years or (10 x 12) = 120 months

Future Value of Initial Deposit = 100000 x (1.007083)^(120) = $ 233255.4468

Monthly Payment = $ 4000 monthly overdue (end of the month)

Let the number of monthly payments be N

Therefore, 233255.4468 = 4000 x (1/0.007083) x [1-{1/(1.007083)^(N)}]

1/(1.007083)^(N) = 0.58696

(1.007083)^(N) = 1/0.58696 = 1.70368

N = = 75.487 months ~ 75 months

Amount Paid in 75 months = 4000 x (1/0.007083) x [1-{1/(1.007083)^(75)}] = $ 232112.8263

Amount Outstanding = 233255.4468 - 232112.8263 = $ 1142.6205

Let the final payment be $ K

Therefore, 1142.6205 = K / (1.007083)^(76)

K = 1142.6205 x (1.007083)^(76) = $ 1953.719