Question

You are considering two loans to finance a purchase of a property valued at $100,000 at LTV of 70%.

Loan A is a fixed-rate mortgage with amortization term of 30 years. The annual interest rate is 8% and the payments are made monthly. Prepayment penalty if the loan is paid off within first 10 years is 3%.

Loan B is an adjustable rate mortgage with an amortization term of 30 years. The initial rate is 4%, but the rate is projected to reset to 8% next year, and 12% the year after. The prepayment penalty if the loan is paid off within first 10 years is 1.5%

Origination fee on both loans is $2,000 and charged up front.

Your holding period for the property is 3 years, at which time you hoping to sell the property at a profit. What is the amount due to lender at the end of 3 years, if you choose loan A?

What is the amount due to lender at the end of 3 years, if you choose loan B?

What would the amount due from you at closing, if you obtain no additional loans, if you choose loan A?

What would the amount due from you at closing, if you obtain no additional loans, if you choose loan B?

Answer 1

Property Value : $100,000 ; LTV = 70% ; Origination fee = $2000 ;

Monthly Mortgage Payment formula = ; and

Residual Loan Balance formula =

where r is the monthly interest rate , t is the loan tenure in months and k is the time period in months at which the loan balance is being calculated.

Loan A : r = 8%/12 = 0.67% ; t = 30 * 12 = 360 months

Loan Balance after 3 years (36 months) = 70000 * [(1+0.67%)³⁶⁰ - (1+0.67%)³⁶] / [(1+0.67%)³⁶⁰ -1] = $68096.1

Prepayment penalty = 3% * 68096.1 = $2042.88

Total due at the end of 3 years = $ 70138.99

At the loan closing (availment of loan), the net loan (after the origination fee) will be $68000. Hence amount due from the borrower for purchase of property will be = $ 32000

Loan B : r₁ = 4%/12 = 0.33% ; r₂ = 8%/12 = 0.67% ; r₃ = 12%/12 = 1% ; Loan term = 360 months

Loan Balance after 1 year (12 months) = 70000 * [(1+0.33%)³⁶⁰ - (1+0.33%)¹²] / [(1+0.0.33%)³⁶⁰ -1] = $68767.27

Loan Balance after 2 year (24 months) = 68767.27 * [(1+0.67%)³⁴⁸ - (1+0.67%)¹²] / [(1+0.67%)³⁴⁸ -1] = $68139.9 (note that since this is the second year of the loan, the residual tenure has been adjusted from 360 months to 348 months)

Loan Balance after 3 year (36 months) = 68139.9 * [(1+1%)³³⁶ - (1+1%)¹²] / [(1+1%)³³⁶ -1] = $67823.49

Prepayment penalty = 3% * 67823.49 = $2034.70

Total due at the end of 3 years = $ 69858.20

At the loan closing (availment of loan), the net loan (after the origination fee) will be $68000. Hence amount due from the borrower for purchase of property will be = $ 32000