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Can someone explain the steps for how to get this answer I have provided for the...

Can someone explain the steps for how to get this answer I have provided for the question? Formulas would be appreciated too.

On the following loan, what is the best estimate of the effective borrowing cost if the loan is prepaid in six years?

Loan:$100,000

Interest rate: 7%

Term:180 months

Up-front costs: 7% of loan amount

Answer: 8.7%

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Answer #1

Monthly payment calculation: PV = -100,000; N = 180; rate = 7%/12 = 0.58%, solve for PMT

PMT = 898.83

Now, if the loan is prepaid in 6 years (or 72 months) then the Future Value (FV) of the mortgage needs to be calculated:

PV = -100,000; PMT = 898.83; N = 72; rate = 0.58%, solve for FV. FV = 71,870.17

The actual loan amount is 100,000*(1-7%) = 93,000 so the effective borrowing rate will be the interest paid on 93,000 for 72 months with the FV of 71,870.17.

PV =-93,000; PMT = 898.83; FV = 71,870.17; N = 72, solve for RATE.

Monthly rate = 0.725%, so annual rate (or effective borrowing rate) is 0.725%*12 = 8.70%

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