Question

QUESTION 2: LOAN AMORTIZATION [35 MARKS] Please answer iii only. I already have the answer for i and ii.

I. A family buys a house worth $326,000. They pay $75,000 deposit and take a mortgage for the balance at J12=9% p.a. to be amortized over 30 years with monthly payments. A. Find the value of the mortgage on their house? (1 mark) B. Find the value of the monthly payment? C. Find the loan outstanding after making 20 payments? D. Find the principal repaid in the 21st payment?

II. Fill out the loan amortization schedule provided in the solution template for the first 5 loan payments. What do you notice about the composition of the payment amount?

III. Suppose that after making 50 payments, the interest rate changes to J2=9% p.a.: A. Convert the interest rate J2=9% to J12 equivalent (2 marks B. Assuming that the family seeks to accept the change in interest rates, what would be their new payment based on the new interest rate? C. Assuming that the family seeks to continue their initial monthly payment calculated in part I, how many full payments would be required to pay off the loan and what would be the final concluding smaller payment one period later?

Answer 1

Solution :- (i)

Interest Rate per month = 9% / 12 = 0.75%

Total Payments in 30 Years = 30 * 12 = 360

Amount Mortgage = $326,000 - $75,000 = $251,000

Therefore Monthly Payments = $251,000 / PVAF ( 0.75% , 360 )

= $251,000 / 124.282

= $2,019.61

(iii) After 50 Payments , Payments Remaining = 360 - 50 = 310

Now Loan Outstanding = $2,019.61 * PVAF ( 0.75% , 310 )

= $2,019.61 * 120.1819

= $242,720.65

Now New Effective interest rate per month = ( 1 + 0.09 / 2 ) ^2/12 = 1.007363 - 1 = 0.7363%

Now therefore J12 = 0.7363% * 12 = 8.836%

Now New Monthly Payment = $242,720.65 / PVAF ( 0.7363% , 310 )

= $242,720.65 / 121.8398

= $1,992.13

Now if Company use old monthly payments = $2,019.61 * PVAF ( 0.7363% , n ) = $242,720.65

$2,019.61 * PVAF ( 0.7363% , n ) = $242,720.65

PVAF ( 0.7363% , n ) = 120.1819

[ 1 - ( 1 + 0.007363 )^-n ] / 0.007363 = 120.1819

( 1 + 0.007363 )^-n = 0.115086

( 1.007363 )ⁿ = 8.689185

Take log Both Sides

n log ( 1.007363 ) = Log ( 8.689185 )

n = 249.72

Approx 250 monthly Installments

If there is any doubt please ask in comments

Thank you please rate