Question

An investment with an initial deposit of $12,993 is growing at an interest rate of 3.22% compounded quarterly. Round all answers to two decimal places if necessary.

1. Find the accumulated amount of the investment at the end of 3 years.

2. The interest rate changes to 4.85% compounded monthly after the first 3 years. Calculate the accumulated amount in this investment at the end of year 6.

3. Find the total amount of interest accumulated during the entire 6 years of the investment.

Answer 1

Answer to Requirement 1.
Initial deposit (Present Value) = $12,993
Interest rate (r ) = 3.22% p.a. or 0.805% per quarter
Time (n ) = 3 years or 12 quarters
Accumulated amount (Future Value) = ??

Future Value = Present Value * (1 + r ) ^ n
Future Value = $12,993 * (1 + 0.00805)^ 12
Future Value = $12,993 * 1.00805^ 12
Future Value = $12,993 * 1.10099
Future Value = $14,305.16

The accumulated amount of the investment at the end of 3 years will be $14,305.16

Answer to Requirement 2.
Amount deposited at the end of Year 3 (Present Value) = $14,305.16
Interest rate (r ) = 4.85% p.a. or 0.4042% per month
Time (n ) = 3 years or 36 months
Accumulated amount at the end of Year 6 (Future Value) = ??

Future Value = Present Value * (1 + r ) ^ n
Future Value = $14,305.16 * (1 + 0.004042)^ 36
Future Value = $14,305.16 * 1.004042^ 36
Future Value = $14,305.16 * 1.15628
Future Value = $16,540.77

The accumulated amount of the investment at the end of 6 years will be $16,540.77

Answer to Requirement 3.
Interest accumulated = Investment accumulated amount – Amount deposited
Interest accumulated = $16,540.77 - $12,993.00
Interest accumulated = $3,547.77