Question

A $36,000 mortgage taken out on June 1 is to be repaid by monthly payments rounded up to the nearest $10. The payments are due on the first day of each month starting July 1. The amortization period is 8 years and interest is 7.1 % compounded semi-annually for a six-month term. Construct an amortization schedule for the six-month term.

What is the monthly payment rounded up to the nearest $10?

Payments= $

Answer 1

The interest rate provided is compunded semiannualy, we need to find out the interest compounded monthly

(1 + 0.071/2)^2 = ( 1 + i)^12

i = 0.5831% ie 7% compounded monthly

installments value can be found out using Present value of annuity formula

Present value of annuity =payments * [ 1 - (1 + periodic interest rate ) ^ - no of periods ] / periodic interest rate

periodic interest rate = 0.5831

no of periods = 8*12 = 96

36000 = payments [ 1 - 1.005831^-96 ] / 0.005831

Payments = 36000 / 73.36 = 490.76

monthly payment = $ 490

Amortisation schedule

Months	Beginning value of loan (a)	Interest ( b = a*0.005831)	Installment ©	Principal portion in Payments (d = c -b)	Closing value of Loan (e = a - d )
1	$36,000.0000	$209.9160	$490.7600	$280.8440	$35,719.1560
2	$35,719.1560	$208.2784	$490.7600	$282.4816	$35,436.6744
3	$35,436.6744	$206.6312	$490.7600	$284.1288	$35,152.5456
4	$35,152.5456	$204.9745	$490.7600	$285.7855	$34,866.7601
5	$34,866.7601	$203.3081	$490.7600	$287.4519	$34,579.3082
6	$34,579.3082	$201.6319	$490.7600	$289.1281	$34,290.1802