Question

Borrow $250,000 at 3% (with monthly compounding). The borrower is required to make monthly interest payments on the loan as well as make monthly deposits into sinking fund earning 6% (monthly compounding) to repay the loan in 15 years. What is the total amount paid each month?

Answer 1

Monthly interest payment = Loan amount x periodic rate

                                            = $ 250,000 x 0.03/12

                                           = $ 250,000 x 0.0025 or $ 625

Formula for FV of annuity can be used to compute monthly payment in to sinking fund as:

FV = P x [(1+r) n -1]/r

P = FV/[(1+r) n -1]/r

FV = Future value of deposits = $ 250,000

P = Periodic cash deposit

r = Rate of return = 0.06 p.a. or 0.06/12 = 0.005 p.m.

n = Number of periods = 12 x 15 = 180

P = $ 250,000/ [(1+0.005) 180 -1]/0.005

    = $ 250,000/ [(1.005) 180 -1]/0.005

    = $ 250,000/ [(2.45409356224715-1)/0.005]

   = $ 250,000/ [(1.45409356224715/0.005)

    = $ 250,000/ 290.818712449429

    = $ 859.642070121168 or $ 859.64

Total payments in a month = $ 625 + $ 859.64 = $ 1,484.64