Question

2. Riley purchases a home and borrows $200,000. Mortgage payments are to be made monthly for 30 years with the first payment to be made one month from loan origination. The annual effective rate of interest is 5%. Starting with 100" payment, $400 is added to each payment in order to repay the mortgage earlier. a. What is the amount of the original monthly payment? b. What is the outstanding balance immediately after the 99 payment? c. What will be the amount of the 100 payment? d. How many more payments in addition to the original 99 payments will be required? e. What will be the amount of last payment?

Answer 1

Principal loan 200000 Repayments are to be made monthly for 30 years with effective annual interest rate of 5%. After 100th payment, $400 is added to each payment. No. of periodic repayments= 30*12 months = 360 months Periodic interest rate will be annual rate divided by 12. Therefore periodic rate= 0.05/12 0.004166667 or 0.42% Discount factor= [(1+r)^n)-1}/[r(1+r)^n] [(1+0.0042)^360)-1 (0.0042(1+0.0042)^360] 3.521454177 0.018990108 185.4362419 (a) Monthly loan repayment = 200000/185.4362 1078.537819

(b) Outstanding balance after 99th payment= PV(1+r)^n - P{[(1+r)^n-1]/r} = [200000(1+0.0042)199] - 1078.54{[(1+0.0042)^99-1)/0.0042} = 302852.72273956 - 132060.447123245 = 170792.2756 c) Amount of 100th payment = 1078.54 +400 = $ 1478.54 d) In order to find the no. of payments in addition to 99 original payments, Assume required number of payments be n. Monthly mortgage payment=Principal loan*[r(1+r)^n]/{[(1+r)^n)-1} In the above formula, Monthly payment= 1478.54 Principal outstanding= 170792.2756 r= 0.0042 By substituting the values, value of n is found. n= 158 payments e) Amt of last installment= $ 1478.54 *Appropriate rounding off has been done to 2 decimal places in calculations