Mr. and Mrs, Smith wish to purchase a home for $400,000. They have a choice betw

Question

Mr. and Mrs, Smith wish to purchase a home for $400,000. They have a choice between two loans. The first is for 80% of the purchase price with an amortization of 30 years at an interest rate of 4% at a fixed rate of interest for the entire amortization period (CPM), with monthly payments. In order to secure the loan, they must pay a 2% loan discount fee. Alternatively, they can borrow 90% of the purchases price for 30 years fixed at a 5% interest rate, 2 points plus 1 point for private mortgage insurance, and an additional 0.5% for mortage insurance annually until the mortage balance is reduced to 80% of the value of the property. The property is estimated to be increasing in value at 3% per year. Calculate the initial incremental cost of borrowing the additional amount assuming the loans will be held for thirty years. Next calculate the effective interest rate for both assuming the property will be held for five years. When does the loan for the 90% loan to value seenario fall below 80% of value? Show how how you set up the problem, as well as highlighting your solutions. Substantial partial credit will be given for thinking through the problem even if you don't get the exact solution.

Explanation / Answer

Option-1:

Property Value=$400,000

Loan amount=400,000×80%= $320,000

Initial charges (@2%)= $320,000×0.02=$6,400

Option-2:

Property Value=$400,000

Loan amount=400,000×90%= $360,000

Initial charges (@3%)= $360,000×0.03=$10,800

Initial additional cost on option-2= $10,800– $6,400= $4,400

Option-1:

Interest rate (fixed) = 4%

Annual interest= $320,000×0.04= $12,800

Total interest for five years=$12,800×5= $64,000

Option-2:

Interest rate (fixed) = 5%

Annual interest= $360,000×0.05= $18,000

Total interest for five years=$18,000×5= $80,000

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