To purchase a house for $80,000, a new couple has $12,000 available for down pay

Question

To purchase a house for $80,000, a new couple has $12,000 available for down payment. They are considering two options:

Option 1: get a new standard mortgage with 10% APR interest compounded monthly for a 30-year term

Option 2: assume the seller’s old mortgage that has an interest rate of 8.5% APR compounded monthly, a remaining term of 25 years (from an original 30 years), a remaining balance of $35,394. You can obtain a second mortgage for the remaining balance from your credit union, at 12% APR compounded monthly, with a 25-year repayment period.

a) What is the effective rate for option 2 per year?

b) Compute the monthly payments for each option over the life of the mortgage

c) What APR charged by the credit union would make the two financing options equivalent?

Explanation / Answer

Total value= $80,000 downpayment =$12,000

b) Option 1 monthly payment

we can use pmt formuale in excel to get the monthly amount
PMT(rate,nper,pv,fv,type)
rate= 10%/12
nper= 30*12= 360 months
pv=$68,000
FV=
type=0

PMT(10%/12,360,-68,000,,0)=$596.75

Option 2 :

sellers old mortgage:
rate=8.5%/12 nper= 25*12=300 pv=$35,394 type=0
pmt(8.5%/12,300,35394,,0)=$285

second mortage:
rate= 12%/12 nper= 25*12=300 pv=68000-35394=$32,606 type=0
pmt(12%/12,300,32606,,0)=$343.41

a) Effective rate for option 2 is:

68,000= 285(P/A,i,300)+343.41(P/A,i,300)
i=10.35%

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