To purchase a house for $80,000, a new couple has $12,000 available for down pay
ID: 1197939 • Letter: T
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
a)
Effective interest rate for old mortgage = (1+8.5%/12)^12 -1 = 8.8391%
Effective interest rate for Credit Union = (1+12%/12)^12 -1 = 12.6825%
Loan Amount on old mortgage = 35394
Loan amount from credit union = Loan amount required - Loan Amount on old mortgage
Loan amount from credit union = (80000-12000) - 35394
Loan amount from credit union = 32606
Total Loan Amount = 32606 + 35394 = 68000
Annual Interest Expenses if it is normal annual loan = 8.8391%*35394 + 12.6825%*32606
Annual Interest Expenses if it is normal annual loan = $ 7263.77
Effective rate for option 2 per year = Annual Interest Expenses if it is normal annual loan/Total Loan Amount
Effective rate for option 2 per year = 7263.77/68000
Effective rate for option 2 per year = 10.68%
b)
Option 1 :
Monthly payments = pmt(rate,nper,pv,fv)
rate = 10%/12
nper =30*12 = 360
pv = -68000
fv = 0
Monthly payments = pmt(10%/12,360,-68000,0)
Monthly payments = $ 596.75
Option 2 :
Old Mortgage :
Monthly payments = pmt(rate,nper,pv,fv)
rate = 8.5%/12
nper =25*12 = 300
pv = -35394
fv = 0
Monthly payments = pmt(8.5%/12,300,35394,0)
Monthly payments = $ 285
Loan taken remaining balance from credit union :
Monthly payments = pmt(rate,nper,pv,fv)
rate = 12%/12 = 1%
nper =25*12 = 300
pv = -32606
fv = 0
Monthly payments = pmt(1%,300,32606,0)
Monthly payments = $ 343.41
Total Monthly Payment in option 2 = 285 + 343.41
Total Monthly Payment in option 2 = $ 628.41
c)
Effective interest rate for option 1 = (1+10%/12)^12 -1 =10.4713%
Annual Interest Expenses if it is normal annual loan would required = Total Loan amount * Effective interest rate for option 1
Annual Interest Expenses if it is normal annual loan would required =68000*10.4713%
Annual Interest Expenses if it is normal annual loan would required = $ 7120.48
Annual Interest Expenses if it is normal annual loan = 8.8391%*35394 + Effective interest rate of credit union*32606
7120.48= $ 3128.51 + Effective interest rate of credit union * 32606
Effective interest rate of credit union = (7120.48-3128.51)/32606
Effective interest rate of credit union = 12.24%
To make the two financing options equivalent
APR charged by the credit union = ((1+Effective interest rate of credit union)^(1/12) -1)*12
APR charged by the credit union = ((1+12.24%)^(1/12) -1)*12
APR charged by the credit union = 11.60%
Answer
APR charged by the credit union = 11.60%
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