Question

After college, Ms Terri amortizes a loan of $200,000 through a 25 year mortgage at 8% compounded quarterly. Find (a) What should be the quartely payment? (b) what is the total interest charges? (c) What is the principal remaining after 10 years?

Answer 1

Answer a.

Loan amount = $200,000
Time period = 25 years or 100 quarters

Annual interest rate = 8%
Quarterly interest rate = 8% / 4
Quarterly interest rate = 2%

Let quarterly payment be $x

$200,000 = $x/1.02 + $x/1.02^2 + … + $x/1.02^99 + $x/1.02^100
$200,000 = $x * (1 - (1/1.02)^100) / 0.02
$200,000 = $x * 43.098352
$x = $4,640.55

Quarterly payment =$4,640.55

Answer b.

Total amount paid = Number of payments * Quarterly payment
Total amount paid = 100 * $4,640.55
Total amount paid = $464,055

Total interest charges = Total amount paid - Loan amount
Total interest charges = $464,055 - $200,000
Total interest charges = $264,055

Answer c.

Period remaining = 15 years or 60 quarters

Loan outstanding = $4,640.55/1.02 + $4,640.55/1.02^2 + … + $4,640.55/1.02^59 + $4,640.55/1.02^60
Loan outstanding = $4,640.55 * (1 - (1/1.02)^60) / 0.02
Loan outstanding = $4,640.55 * 34.760887
Loan outstanding = $161,309.63