Question

3. A $300,000 home loan is amortized by equal monthly payments for 25 years, starting one month from the time of the loan at a nominal rate of 7% convertible monthly. a. Find the monthly payment amount. b. Find the outstanding balance when 10 years of payments remain. c. Find the total interest paid during the last 10 years of the loan? 4. Eddie is repaying a 20-year loan of 10,000 with payments at the end of each year. Each of the first 10 payments equals 150% of the amount of interest due. Each of the last 10 payments is X. The lender charges interest at an annual effective rate of 10% a. Calculate the outstanding balance after 10 initial payments. b. Calculate X

Answer 1

Because of multiple questions asked, as HOMEWORKLIB's policy only the first question is answered:

Given information

Home loan amount P = $300,000

No. of periods = 25 * 12 = 300 (we are considering monthly payments hence multiple the number of years by 12 months)

interest rate = r = 7% per annum = 7/12 % = 0.5833% monthly

Part a:

Monthly installment payment amount (M) is given by the formula:

M = (P * r) / [1 - (1+r)^-n ]

Substitute the given values = (300,000 * 0.5833 %) / [1 - (1+0.5833 %)^-300 ] = $2120.3376

Part b

Find the outstanding balance when 10 years of payment remain. This means that the last payout was after 20 years i.e. 240 months.

The formula to calculate principal amount remaining after i^th payout is given by:

P(i) = P [ 1 - ((1+r)^t - 1) / ((1+r)ⁿ - 1) ]

So Principal amount remaining after 240th payout =

P(24) = 300000(1-((1+0.5833%)²⁴⁰-1)/((1+0.5833%)³⁰⁰-1)) = $107,078.4298

Part c

Total payment made in last 10 years = monthly payment * 120= 2120.3376*300=254440.511

Principal amount left after 20 years = 107078.4298 hence principal left = 300000 - 107078.4298 = 192921.5702

Hence interest paid in the last 10 years = 254440.511- 192921.5702 = $61,518.9409