Question

Ms. Shannon Sauser bought a house with a market value of $410,000. In order to avoid the mortgage insurance, she put 25% down on it. It is a conventional 15-year fixed the mortgage with 6.5%. Determine the following:

Her monthly payment.

Monthly interest payment on month 10

Monthly principal on month 22

If no prepayments are made, what should be her remaining balance at the end of the 3^rd year?

Suppose Shannon paid $100 extra towards the principal every month from the very first month. On the 18^th month, her remaining balance becomes $286,124.50. What should be her schedule principal and interest payment on the 19^th month?

Answer 1

Market value = $410,000

Loan Value = 75%*410000 = $307,500.00

Interest Rate = 6.5% annual i.e. 6.5%/12 monthly

Loan term = 15 years i.e. 180 months

1) Monthly Payment A = 307500*(6.5%/12)/(1-(1+(6.5%/12))^-180) = $2,678.66

2) Monthly interest payment on month 10

PV of Loan after the 9^th instalment = 2678.66*((1-(1+(6.5%/12))^-171)/(6.5%/12)) = $298,183.21

Hence Interest payment on month 10 = $298,183.21*6.5%/12 = $1,615.16

3) Monthly principal on month 22

PV of Loan after the 21^st instalment = 2678.66*((1-(1+(6.5%/12))^-159)/(6.5%/12)) = $285,034

Hence principal amount on 22^nd instalment = $2678.66-(285034*6.5%/12) = $1,134.73

4) Remaining balance at the end of year 3 i.e. 36 months = 2678.66*((1-(1+(6.5%/12))^-144)/(6.5%/12))

Remaining balance at the end of year 3 = $267,352