You are looking at a one-year loan of $24,000. The interest rate is quoted as 12

Question

You are looking at a one-year loan of $24,000. The interest rate is quoted as 12 percent plus three points. Apoint on a loan is simply 1 percent (one percentage point) of the loan amount. Quotes similar to this one are common with home mortgages. The interest rate quotation in this example requires the borrower to pay three points to the lender up front and repay the loan later with 12 percent interest. What rate would you actually be paying here?

You are looking at a one-year loan of $24,000. The interest rate is quoted as 12 percent plus three points. Apoint on a loan is simply 1 percent (one percentage point) of the loan amount. Quotes similar to this one are common with home mortgages. The interest rate quotation in this example requires the borrower to pay three points to the lender up front and repay the loan later with 12 percent interest. What rate would you actually be paying here?

Explanation / Answer

The PV of the loan = $24,000

Time period = 1 year

Rate = 12 percent plus 3 points.

We need to pay the principal with 12% interest and we need to pay 3% interest upfront.

Hence we need to pay NOW = 0.03 * 24,000 = $720

And after 1 year we will pay 1.12 * 24,000 = $26,880

Now, We have updated PV = $24,000 - $720 = $23,280

FV = $26,880

N = 1

And we will find R by using the formula FV = PV * (1 + r)n

26,880 = 23,280 * (1 + r)1

R = 15.46%

I hope my solution solves your query.

Regards.

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