Finance Business

Question

Holly purchased a house for $325,000. She made a down payment of 25.00% of the value of the house and received a mortgage for the rest of the amount at 5.72% compounded semi-annually amortized over 20 years. The interest rate was fixed for a 5 year period.



a. Calculate the monthly payment amount.

b. Calculate the principal balance at the end of the 5 year term.

c. Calculate the monthly payment amount if the mortgage was renewed for another 5 years at 5.32% compounded semi-annually?

Answer 1

The principal (PV of the loan) is the present value of the monthly payments .

The PV = Payment* (1/i)(1-(1/(1+i))^n) where n is the number of payments. Define M as (1/i)(1+(1/(1+i))^n). We have a 20 year loan with 12 payments per year so n= 240 months. The interst rate is 5.72% which is 5.72%/12 per month = .477%. So M = (12/5.72%)(1+(1/(1+5.72%/12))^240. Which equals 142.781. PV= Paymnet *M so Payment = PV/M we are financing 75% of 325,000 or 243,750. . so Payment = 1707.16.

In 5 years their will be 180 payments left on the mortgage. The PV of those remaining payments is given by PV = 1707.16*(M') where M' is the new discount multiplier with an i of 5.72% and n= 180 = 120.655. so 120.655*1706.16 is 205,978.61 remaining principal on the loan.

Calculating a new payment on the remaining principal we need to calculate M'' with an interest rate of 5.32% M" = 123.829. Dividing the remaining principal by M'' gives a new payment of 1,663.407

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