Question

Your best friend wins the lottery and gives you a gift option.  You need to complete both problems to make your decision.

1. As one gift option, they offer to give you the interest only from a $1,000,000 investment with an interest rate of 8% that compounds annually.  How much interest do you receive in 5 years?

2. As another gift option, they offer to give you the interest only from $2,000,000 investment with an interest rate of 7% that compounds semi-annually.  How much interest do you receive in 2.5 years?

3. What is the future value of $13,000 at 10% compounded semi-annually over 10 years?

4. What is the future value of $13,000 at 10% interest compounded quarterly over 10 years?

Answer 1

Answer:

Option 1:
Amount of Investment = $1,000,000
Rate = 8%
Time = 5 years
Amount to be received after 5 years (Future Value) = ??

Future Value = Present Value * (1 + r)^ n
Future Value = $1,000,000 * (1 + 0.08)^ 5
Future Value = $1,000,000 * 1.08^5
Future Value = $1,000,000 * 1.4693
Future Value = $1,469,300

Interest received = Amount received after 5 years – Amount invested
Interest received = $1,469,300 - $1,000,000
Interest received = $469,300

Option 2:
Amount of Investment = $2,000,000
Rate = 7% or 3.5% semi-annually
Time = 2.5 years or 5 semi-annual periods
Amount to be received after 2.5 years (Future Value) = ??

Future Value = Present Value * (1 + r)^ n
Future Value = $2,000,000 * (1 + 0.035)^ 5
Future Value = $2,000,000 * 1.035^5
Future Value = $2,000,000 * 1.4693
Future Value = $2,375,400

Interest received = Amount received after 2.5 years – Amount invested
Interest received = $2,375,400 - $2,000,000
Interest received = $375,400

Option 3:
Present Value = $13,000
Rate (r ) = 10% or 5% semi-annually
Time (n ) = 10 years or 20 semi-annual periods
Future Value = ??

Future Value = Present Value * (1 + r)^ n
Future Value = $13,000 * (1 + 0.05)^ 20
Future Value = $13,000 * 1.05^ 20
Future Value = $13,000 * 2.6533
Future Value = $34,492.90

Option 4:
Present Value = $13,000
Rate (r ) = 10% or 2.5% quarterly
Time (n ) = 10 years or 40 quarters
Future Value = ??

Future Value = Present Value * (1 + r)^ n
Future Value = $13,000 * (1 + 0.025)^ 40
Future Value = $13,000 * 1.025^ 40
Future Value = $13,000 * 2.6851
Future Value = $34,906.30