Question

THREE FINANCE for BUSINESS QUESTIONS, ~all unrelated to each other

1. Alpha Company invests $15,600 at an interest rate of 14% for five years. What is the difference between simple and compound interests? Assume that in case the interest rate compounds semiannually.

2. Let’s assume there is a firm that wants to invest $34,000 in a project with an interest rate of 9% annually, and that the project will last for twelve years. What will be the interests coming from the project if the firm chooses not to reinvest any of its earnings? Assume the interest rate compounds annually.

3. Let us assume there is a project that will bring in $38,509.42 six years from now, assuming the interest rate of 9.6% that will compound monthly. What is the project’s present value?

Answer 1

Answer to Question 1:
Simple Interest:
Amount Invested (Principal) = $15,600
Interest Rate = 14% or 7% semi-annually
Time = 5 years or 10 semi-annual periods

Simple Interest = Principal * Interest Rate * Time
Simple Interest = $15,600 * 7% * 10
Simple Interest = $10,920

Compound Interest:
Amount Invested (Present Value) = $15,600
Interest Rate (r ) = 14% or 7% semi-annually
Time (n ) = 5 years or 10 semi-annual periods
Value of Investment after 5 years (Future Value) = ??

Future Value = Present Value * (1 + r) ^ n
Future Value = $15,600 * (1 + 0.07)^ 10
Future Value = $15,600 * 1.07^ 10
Future Value = $15,600 * 1.967151
Future Value = $30,687.56

Compound Interest = Value of Investment after 5 years – Amount Invested
Compound Interest = $30,687.56 - $15,600
Compound Interest = $15,087.56

Difference between Simple Interest and Compound Interest = $15,087.56 - $10,920
Difference between Simple Interest and Compound Interest = $4,167.56