This question illustrates what is known as discount interest . Imagine you are d

Question

This question illustrates what is known as discount interest. Imagine you are discussing a loan with a somewhat unscrupulous lender. You want to borrow $20,000 for one year. The interest rate is 12.5 percent. You and the lender agree that the interest on the loan will be .125

This question illustrates what is known as discount interest. Imagine you are discussing a loan with a somewhat unscrupulous lender. You want to borrow $20,000 for one year. The interest rate is 12.5 percent. You and the lender agree that the interest on the loan will be .125

Explanation / Answer

Here, the PV of the loan = $20,000 - $2,500 = $17,500 (As this is the actual amount we are receiving).

FV of the loan = $20,000 (This is amount we need to pay at the end of the period)

N = 1 (Number of year)

As we know, FV = PV * (1 + I/Y)N

$20,000 = $17,500 (1 + I/Y)1

1.1429 = 1 + I/Y

I/Y = 14.29% is the effective interest rate on the loan.

I hope my solution solves your query.

Regards.

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