Question

Please give step by step workings with formulas using the actuarial method. This is especially for part a.

Smithy takes out a $50,000 mortgage on a home at 12% compounded monthly. He is to pay off the mortgage with monthly payments for 20 years, with the first payment due 1 month after the mortgage is taken out.

Find (a) the amount of each monthly payment and (b) construct a partial amortization schedule for the first 4 months of the mortgage.

Answer 1

Please give step by step workings with formulas using the actuarial method.

Mortgage Amt = $50,000
ROI = 12% (compounded monthly)
Term = 20 years, (with the first payment due 1 month after the mortgage is taken out.)

(a) the amount of each monthly payment :
EMI = [P x R x (1+R)^N]/[(1+R)^N-1],
where,
P stands for the loan amount ($50,000),
R is the interest rate per month (12%/12 Month)= 1% and
N is the number of monthly instalments. (20*12= 240 no.)
= [ $50,000 * 1% *( 1 + 1%)240] / [(1+1%)240-1]
= $500 *10.8926 / 9.8926
= $5446.30 / 9.8926
= $550.54 or say 551 (in Round Off)

(b) construct a Partial amortization schedule for the first 4 months of the mortgage.

No. of Month	Opening Balance	Payment	Interest	Principal	Balance @ End
1	$50,000	$551.00	$500.00	$51.00	$49,949.00
2	$49,949.00	$551.00	$499.49	$51.51	$49,897.49
3	$49,897.49	$551.00	$498.97	$52.03	$49,845.46
4	$49,845.46	$551.00	$498.45	$52.55	$49,792.92
5	$49,792.92	$551.00	$497.93	$53.07	$49,739.85
6	$49,739.85	$551.00	$497.40	$53.60	$49,686.25