Question

Ann took a $12,000 loan at an interest of 12 % compounded bi-monthly. He needs to pay it over 5 years.

Construct the amortization schedule on this loan for the first three bi-monthly payments.

Answer 1

Loan amount = $12,000

Loan frequency = bi-monthly

Annual interest rate = 12%

Bi-monthly interest rate = Annual interest rate / 24 = 12%/24 = 0.5%

Loan period = 5 years = 5*24 bi-monthly periods = 120 bi-monthly periods

The present value of an ordinary annuity is given by the formula

Here, PV = loan amount = $12,000

C = bi-monthly loan payment

i = bi-monthly interest rate = 0.5%

n = loan period = 120 bi-monthly periods

$12,000 = C * 90.07345333

C = $12,000 / 90.07345333 = $133.22

Bi-monthly loan payment = $133.22

The amortization schedule for the first 3 payments is shown below

Period is the bi-monthly period

Interest Payment = Bi-monthly Interest Rate *Loan Opening Balance

Principal Payment = Bi-Monthly Loan Payment - Interest Payment

Loan Closing Balance = Loan Opening Balance - Principal Payment

Initial Loan Opening Balance = $12,000

Subsequent Loan Opening Balance = Loan Closing Balance for the previous period