Question

John plans to borrow $400,000 15-years mortgage loan from his bank, which agrees that

     John should repay the loan in 180 equal end-of-month payments. The annual interest

     rate is 4%, compounded monthly.   

     (1) What is the amount of each monthly payment? Show your calculation.

(2) How much total interest dollar amount will John pay over the 180 months life of the

       loan?   Show your calculation

(3) Complete the following loan amortization schedule for the first 6 months.

       Rounding amounts to the nearest dollar                                                   (20 points)

Month              Monthly                Dollar                 Principal                Ending

                        Payment               Interest                  Payment              Balance

0                                                                                                           $400,000

1              

2

3

4

5

6

Answer 1

(a)-Monthly Loan Payment

Loan Amount (P) = $400,000

Monthly Interest Rate (n) = 0.33333333% per month [4.00% / 12 Months]

Number of months (n) = 180 Months [15 Years x 12 Months]

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

= [$400,000 x {0.0033333333 x (1 + 0.0033333333)¹⁸⁰}] / [(1 + 0.0033333333)¹⁸⁰ – 1]

= [$400,000 x {0.0033333333 x 1.820301627}] / [1.820301627 – 1]

= [$400,000 x 0.006067672] / 0.820301627

= $2,427.09 / 0.820301627

= $2,958.75

(b)-Total Interest paid for the Loan

Total Interest for the Loan = Total Payment – Loan Amount

= [$2,958.75 x 180 Months] - $400,000

= $532,575.00 - $400,000

= $132,575.00

(c)-Loan amortization schedule for the first 6 months.

Month	Monthly payment	Dollar interest	Principal payment	Ending balance
0	0	0	0	4,00,000
1	2,959	1,333	1,625	3,98,375
2	2,959	1,328	1,631	3,96,744
3	2,959	1,322	1,636	3,95,107
4	2,959	1,317	1,642	3,93,466
5	2,959	1,312	1,647	3,91,819
6	2,959	1,306	1,653	3,90,166