Alternatively PFert P tells you the most you should loan Exa

Alternatively, P=F/e^rt. P tells you the most you should loan. Example: if a borrower tells you that he will give you back $141.02 at the end of a loan for six years and three months with an interest rate of 5 ½% per annum. The most you would have loaned him was P equals $100. Here is a loan proposition more in line with the current interest rates. A borrower agrees to pay you 4 ¾% annually for the next seven years and 6 six months. At the end of the term, he will make a balloon payment of $20,000 to repay the loan and the interest. What amount (P) should you loan this prospect?

Solution

The amount (P) that should be loaned is calculated as below:

Here, F = $20,000, r = 4.75% and t = 7.5 years

Substituting these values in the formula provided in the question, we get,

P = 20,000/e^(4.75%*7.5)

We can use the exp (exponential function of EXCEL) to arrive at the value of e or take e = 2.718. Solving further we get,

P = 20,000/(2.718^(4.75%*7.5)) = $14,006.47 or $14,006 (answer)

The amount (P) that should be loaned to this prospect is $14,006.