For each situation determine the present value and the inter

For each situation, determine the present value and the interest earned:

a) A loan of $21 500 is due in 6 years. The interest rate is 8%/a, compounded quarterly.

b) A loan of $ 100 000 is due in 5 years. The interest rate is 5%/a, compounded semi-annually.

Solution

I guess by loan due you mean amount due, or in the two cases the amount that has to be paid at the end of 6 and 5 years respectively is $21500 and $100000 respectively.

In the first case the interest earned is 21500*( 1+ .02)^24 - 21500 = $13081.4

The present value of the $21500 in the first case is 21500/ (1.02^24) = $13367. This means that paying $12500 after 6 years is the same as paying $13367 now.

In the second case the interest earned is 100000*(1+.025)^10- 100000 = 28008.45

The present value here is 100000/ (1.025^10) = $78119.8