Question

Catherine received a 30 year loan of $240,000 to purchase a house. The interest rate on the loan was 5.90% compounded monthly.

a. What is the size of the monthly loan payment?

$

Round to the nearest cent

b. What is the principal balance of the loan at the end of 3 years?$

Round to the nearest cent

c. By how much will the amortization period shorten if Catherine made an extra payment of $54,000 at the end of the year 3?

years

months

Express the answer in years and months, rounded to the next month

Answer 1

a.

Calculating Monthly Payment,

Using TVM Calculation,

PMT = [PV = 240,000, FV 0, N = 360, I = 0.059/12]

PMT = $1,423.53

b.

Calculating Loan Balance at the end of Year 3,

Using TVM Calculation,

FV = [PV = 240,000, PMT = -1,423.53, N = 48, I = 0.059/12]

FV = $226,852.24

c.

Loan Balance after $54,000 payment = 226,852.24 - 54,000 = $172,852.24

Calculating Time Period,

Using TVM Calculation,

N = [PV = 172,852.24, FV = 0, PMT = -1,423.53, I = 0.059/12]

N = 185.30

Shortening of Time = (360 - 48) - 185.30

Shortening of Time = 127 months

Shortening of Time = 10 years 7 months