PLEASE SHOW WORK A fully amortizing loan has the following terms and conditions:

Question

PLEASE SHOW WORK

A fully amortizing loan has the following terms and conditions:

Interest Rate: 6% per annum

Term: 20 years

Original Loan Amount:    $395,000

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?

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

1.) Interest Rate: 6% per annum

Original Loan Amount: $395,000

Term: 20 years

Monthly Installment of Loan =PMT(0.005,240,395000) =$2,829.90

Let the lender charge X amount to make his yield =6.5% or monthly 0.5417%

Equating Cash flows

395,000 = X + 2,829.90x{(1-(1+0.005417)-240)/0.005417}

395,000 = X + 2,829.90x134.125

X = 395,000 - 379,560.71

X =$15,439.29

Dollars to be charged for Points =$15,439.29

Hence, the points to be charged =15,439.29/395,000x100 =3.908%

2.) Loan outstanding at the end of 10th year =$254,899

Since this amount will be paid off in a single installment, the yield for the lender is 6.5%

Equating Cash flows,

395,000 = X + 2,829.90x{(1-(1+0.005417)-120)/0.005417} + 254,899/(1+0.005417)120

395,000 = X + 2,829.90x88.0685 + 133,302.56

X = 395,000 - 249,225.28 + 133,302.56

X =$12,472.15

Dollars to be charged for Points =$12,472.15

Hence, the points to be charged =12,472.15/395,000x100 =3.1575%

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