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

·Option 1:

i = 10%/12 = 0.8333% per month, N = 360 months

·Option 2: For the assumed mortgage,

P1= $35,394, i1= 8.5%/12 = 0.70833% per month,

N1= 300 months, A1= $285 per month;

For the second mortgage,

P2= $32,606, i2= 1% per month,

N2= 120 months,A2= $32,606(A/P, 1%, 120) = $467.80

(a)For the second mortgage, the monthly payment will be

$68,000 = $285(P/A, i, 300) + $467.81(P/A, i, 120)

i = 0.80744% per month

r = 0.80744%*12 = 9.6893% per year

ia= 10.1314% per year

(b)Monthly payments:

·Option 1:A1= $68,000(A/P, 0.8333%, 360) = $596.32

·Option 2: $752.81 for 120 months, then $285 for remaining 180 months

(C)Equivalent interest rate:

$596.32(P/A, i, 360) = $285(P/A, i, 300) + $467.81(P/A, i, 120)

i = 0.8954% per month

r = 0.8954%*12 = 10.7448% per year

ia= 11.29% per year

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