FINA 300 Help on Interest

Question

A couple has just purchased a home for $371,600.00. They will pay 20% down in cash, and finance the remaining balance. The mortgage broker has gotten them a mortgage rate of 5.64% APR with monthly compounding. The mortgage has a term of 30 years.

How much interest is paid in the first year?

Answer 1

The house is 371,600. The put down 20% or or 71,120 which leaves 296,480 to be financed The mortgage is for 30 or 360 months. The annual interest rate is 5.64% APR or .47% per month. The present Value of the payments is Given by

PV+ Payment*(PV Multiplier) The PV Multiplier or PVM(n,i) is (1/i)1-(1/(1+i))ⁿ depends on the number of payments, n and the periodic (here monthly interest rate)

PV (360,.47%) = (1/.0047)(1- (1/(1.0047))³⁶⁰) = (/.0047)*(1-.18488) = 173.42

So loan amount or PV = 296,480 = Payment*173.42 or Payment = 296,480/173.42 = 1,703.51 per month.

Now comes the tricky part in 1 year the will be 348 paymnets left. So me calculate the new Payment multiplier to determine the present value (in 12 months) of the remaining 348 payments. This will be the principal remaining on the loan. New Multiplier PVM(348,.47%)

or (1/.0047)(1-(1/(1.0047))³⁴⁸ = 171.152 so the principal remaining will be 171.52*1703.51 =291,559.93. soooo, they have knocked the principal of 296,480 down by 4,920.06. The have mad a total of 12 payment ,s of 1,703.51 or 20,514.18 in payments so the difference is 15,594.11 they have paid in interest

I hope this helps