Compare the interest earned by P dollars at i per year simpl

Compare the interest earned by P dollars at i% per year simple interest with that earned by the same amount P for five years at i% compounded annually.

Solution

Simple Interest = Principal x Interest Rate x Term of the loan

= P x i x n

Thus, if simple interest is charged at 5% on a $10,000 loan that is taken out for a five year period, the total amount of interest payable by the borrower is calculated as: $10,000 x 0.05 x 5= $2,500.

Compound Interest = Total amount of Principal and Interest in future (or Future Value) less Principal amount at present (or Present Value)

= [P (1 + i)ⁿ] – P

= P [(1 + i)ⁿ – 1]

Continuing with the above example, what would be the amount of interest if it is charged on a compound basis? In this case, it would be: $10,000 [(1 + 0.05)⁵] – 1 = $10,000 [1.2762815625– 1] = $2,762.815625.