Questions: Given a 7.25 percent interest rate, compute the year 7 future value of deposits made in years 1, 2, 3, and 4 of 1,100, 1,300, 1,600, and 1,600.

Solution Steps

To find the future value of each deposit, we need to calculate how much each deposit will grow by year 7 using the formula for future value: \( FV = PV \times (1 + r)^n \), where \( PV \) is the present value (initial deposit), \( r \) is the interest rate, and \( n \) is the number of years the money is invested. We will calculate the future value for each deposit separately and then sum them up to get the total future value by year 7.

We will calculate the future value (FV) of each deposit made in years 1, 2, 3, and 4 by year 7 using the formula:

\[ FV = PV \times (1 + r)^n \]

where:

• \( PV \) is the present value (the amount deposited),
• \( r = 0.0725 \) is the interest rate,
• \( n \) is the number of years until year 7.

Calculating for each deposit:

• For the deposit of \$1,100 made in year 1 (6 years until year 7): \[ FV_1 = 1100 \times (1 + 0.0725)^6 \approx 1674.0811 \]

• For the deposit of \$1,300 made in year 2 (5 years until year 7): \[ FV_2 = 1300 \times (1 + 0.0725)^5 \approx 1844.7175 \]

• For the deposit of \$1,600 made in year 3 (4 years until year 7): \[ FV_3 = 1600 \times (1 + 0.0725)^4 \approx 2116.9431 \]

• For the deposit of \$1,600 made in year 4 (3 years until year 7): \[ FV_4 = 1600 \times (1 + 0.0725)^3 \approx 1973.8397 \]

Now, we sum the future values of all deposits to find the total future value by year 7:

\[ \text{Total Future Value} = FV_1 + FV_2 + FV_3 + FV_4 \]

Calculating the total: \[ \text{Total Future Value} \approx 1674.0811 + 1844.7175 + 2116.9431 + 1973.8397 \approx 7609.5814 \]

Final Answer