Question

Steve Martin deposited $300,000 into an investment that earned 4.55% compounded quarterly for the first 4 years. It was then reinvested to earn 5.65% compounded monthly for the next 3 years 5 months. Determine the maturity value of his investment. A proper timeline is required for full mark

Answer 1

To determine the maturity value of Steve Martin's investment, we need to calculate the value after each compounding interval and add them up. The investment earns 4.55% compounded quarterly for the first 4 years and then earns 5.65% compounded monthly for the next 3 years and 5 months.

Step-by-step explanation:

Timeline for the Investment

1. First 4 years: Quarterly compounding at 4.55%
2. Year 5: Monthly compounding at 5.65%
3. Year 6: Monthly compounding at 5.65%
4. Year 7: Monthly compounding at 5.65%
5. 5 months: Monthly compounding at 5.65%

Calculation for the Maturity Value

Step 1: Calculate the maturity value after 4 years using the quarterly compounding formula:

Principal Accumulated = Principal * (1 + (Annual Interest Rate / Number of Compounding Periods))^(Number of Compounding Periods * Number of Years)

Step 2: Calculate the maturity value after each subsequent year using the monthly compounding formula and add it to the previous value:

Maturity Value = Maturity Value After 4 Years * (1 + (Monthly Interest Rate / 100))^(Number of Compounding Periods * Number of Years)

Step 3: Calculate the maturity value after the 5 months using the monthly compounding formula:

Maturity Value After 5 Months = Maturity Value After 7 Years * (1 + (Monthly Interest Rate / 100))^(Number of Compounding Periods * Number of Years)

Step 4: Add all the maturity values obtained in the previous steps to get the final maturity value of the investment.