Question

John plans to borrow $400,000 from his bank, which agrees that John should repay the loan in 180 equal end -of-months payments. The annuel interest rate is 4.5%, compounded monthly.

(1) what is the amount of each monthly payment? show your calculation

(2) How much is the total interest in dollars amount will John pay over a 15 year life of the loan? Show your calculation

(3) complete the following loan amortization schedule for the first 6 months and the last month. Rounding amounts to the nearest dollar.

Answer 1

1

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

400000= Cash Flow*((1-(1+ 4.5/1200)^(-15*12))/(4.5/1200))

Cash Flow = 3059.97 = monthly payment

2

Total interest = monthly payment*numlber of months-principal = 3059.97*180-400000=150794.6

3

	Monthly rate(M)=	yearly rate/12=	0.38%	Monthly payment=	3059.97
Month	Beginning balance (A)	Monthly payment	Interest = M*A	Principal paid	Ending balance
1	400000.00	3059.97	1500.00	1559.97	398440.03
2	398440.03	3059.97	1494.15	1565.82	396874.20
3	396874.20	3059.97	1488.28	1571.69	395302.51
4	395302.51	3059.97	1482.38	1577.59	393724.92
5	393724.92	3059.97	1476.47	1583.50	392141.42
6	392141.42	3059.97	1470.53	1589.44	390551.97
180	3048.54	3059.97	11.43	3048.54	0.00

Where

Interest paid = Beginning balance * Monthly interest rate

Principal = Monthly payment – interest paid

Ending balance = beginning balance – principal paid

Beginning balance = previous Month ending balance