Question

A couple has just purchased a home for $327,400.00. They will pay 20% down in cash, and finance the remaining balance. The mortgage broker has gotten them a mortgage rate of 5.64% APR with monthly compounding. The mortgage has a term of 30 years.

How much interest is paid in the first year?

Answer Format: Currency: Round to: 2 decimal places.

Answer 1

Monthly Loan Payment

Loan Amount (P) = $261,920 [$327,400 x 80%]

Monthly Interest Rate (n) = 0.47% per month [5.64% / 12 Months]

Number of months (n) = 360 Months [30 Years x 12 months]

Monthly Loan Payment = [P x {r (1+r)ⁿ} ] / [( 1+r)ⁿ – 1]

= [$261,920 x {0.0047 x (1 + 0.0047)³⁶⁰}] / [(1 + 0.0047)³⁶⁰ – 1]

= [$261,920 x {0.0047 x 5.408848] / [5.408848 – 1]

= [$261,920 x 0.025422] / 4.408848

= $6,658.43 / 4.408848

= $1,510.24 per month

Monthly Loan Amortization Schedule

Month	Beginning Amount ($)	Total Payment ($)	Interest Payment at 0.47% ($)	Principal Payment ($)	Ending Balance ($)
1	2,61,920.00	1,510.24	1,231.02	279.22	2,61,640.78
2	2,61,640.78	1,510.24	1,229.71	280.53	2,61,360.26
3	2,61,360.26	1,510.24	1,228.39	281.85	2,61,078.41
4	2,61,078.41	1,510.24	1,227.07	283.17	2,60,795.24
5	2,60,795.24	1,510.24	1,225.74	284.50	2,60,510.74
6	2,60,510.74	1,510.24	1,224.40	285.84	2,60,224.90
7	2,60,224.90	1,510.24	1,223.06	287.18	2,59,937.71
8	2,59,937.71	1,510.24	1,221.71	288.53	2,59,649.18
9	2,59,649.18	1,510.24	1,220.35	289.89	2,59,359.29
10	2,59,359.29	1,510.24	1,218.99	291.25	2,59,068.04
11	2,59,068.04	1,510.24	1,217.62	292.62	2,58,775.42
12	2,58,775.42	1,510.24	1,216.24	294.00	2,58,481.42
TOTAL			14,684.30

“Hence, the total interest is paid in the first year will be $14,684.30”