A fully amortizing loan has the following terms and conditions: Interest Rate: 6

Question

A fully amortizing loan has the following terms and conditions:

Interest Rate: 6 % per annum

Term: 20 years

Original Loan Amount: $395,000

1) If the lender expects the loan to be paid over the entire 20-year term, how many points (in dollars and in percentage terms) would the lender have to charge to achieve a 6.5% yield on this loan?

2) If the lender expects the loan to be paid off with a single lump-sum, additional principal payment at the end of the 10th year, how many points (in dollars and in percentage terms) would the lender have to charge to achieve a 6.5% yield on this loan?

Explanation / Answer

Now loan amount is $395,000 and let x% is charged upfront as a fees. Lets first calculate the Per year payment to completely pay off this loan

PV = 395000; n = 20; 1/y = 6%; FV = 0; calculate PMT = $34,437.9

Now PMT = 34,437.9; n=20; FV = 0; 1/y = 6.5%; Calculate PV = $379,454.25

Now this PV must be equal to $395,000. So the shortfall is $15,545.75 which needs to be charged upfront so that 6.5% is earned.

so $15,545.75 needs to be charged OR 3.94% of principle amount.

2) If the lender expects the loan to be repaid in single lump sum at the end of 10th year. Loan maturity value at 6% for 10 years will be 395000*1.06^10 = $707,384.84

Now discounting the same amount at 6.5%, gives the present value = 707384.84 / 1.065^10 = $376,842.32

Now this is short by $18,157.67 from original $395,000. So $18,157.67 needs to be charged OR 4.6% needs to be charged upfront to get the 6.5% yield on the loan.

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