Answer to Question #142857 in Financial Math for tineiafi

Question

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? (2 mark)
B. Find the value of the monthly payment? (4 marks)
C. Find the loan outstanding after making 20 payments? (4 marks)
D. Find the principal repaid in the 21st payment? (5 marks)

Answer 1

Mortgage value(MV)= House price-Deposit Amount

A. MV= $326,000-$75, 000= $251,000

B. Value of monthly payment

T= 30 years

$T months=30\times12 =360 months$

Monthly payments$=\frac {251,000\times 0.75\times 1.075^{360}}{1.0075^{360}-1}$ = $2019.6

C. Loan outstanding after making 20payments= $\frac {2019.6\times (1-1.0075^{-340})}{0.0075}$

Loan outstanding = $ 248,053.2

D. Principal repaid in the 21st payment

Principal = P₃₄₀-P₃₃₉

P₃₃₉ =$\frac {2019.6\times(1.1.0075^{-339}}{0.0075}$

The principal paid in the 21^st payment = $248,053.15 - $247,893.95

P₂₁ = $ 159.20