To purchase a house for $80,000, a new couple has $12,000 available for down pay
ID: 1198242 • 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)
Amount of Loan Required =80000-12000 = 68000
Effective interest rate for old Mortgage = (1+APR/12)^12-1
Effective interest rate for old Mortgage = (1+8.5%/12)^12-1
Effective interest rate for old Mortgage = 8.84%
Effective Interest rate from your credit union, = (1+APR/12)^12-1
Effective Interest ratefrom your credit union, = (1+12%/12)^12-1
Effective Interest rate from your credit union,= 12.6825%
Effective rate for option 2 per year = 8.84*35394/68000 + 12.6825*(68000-35394)/68000
Effective rate for option 2 per year = 10.68%
b)
Option 1
Monthly payments = Loan Amount/((1-(1+r)^-n)/r)
Monthly payments = 68000/((1-(1+10%/12)^-360)/(10%/12))
Monthly payments = $ 596.75
Option 2
Monthly Payment of old Mortgage = Old Mortgage balance/((1-(1+r)^-n)/r)
Monthly Payment of old Mortgage = 35394/((1-(1+8.5%/12)^-300)/(8.5%/12))
Monthly Payment of old Mortgage = 285
Monthly Payment from union credit = Loan amount from your credit union,/((1-(1+r)^-n)/r)
Monthly Payment from union credit =(68000-35394)/((1-(1+12%/12)^-300)/(12%/12))
Monthly Payment from union credit = 343.41
Total Monthly Payment = 285 + 343.41
Total Monthly Payment = $ 628.41
c)
Effective rate for option 1 = (1+APR/12)^12-1
Effective rate for option 1 = (1+10%/12)^12-1
Effective rate for option 1 = 10.47%
Two financing options equivalent when thier Effective rate are equal
Effective rate of credit union = (10.47% - 8.84%*35394/68000 ) * 68000/(68000-35394)
Effective rate of credit union = 12.24%
APR charged by the credit union =( (1+Effective 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%
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