Questions: Raj comes across a 7-year investment option that provides a 10% interest rate with a monthly deposit of 500. Which type of TVM calculation will help Raj determine the amount of money he will have after 7 years? Calculating the future value of 50,000 invested today Calculating the present value for an annuity of 500 Calculating the future value for an annuity of 500 Calculating the present value for the expected earnings of 50,000

Solution Steps

To determine the amount of money Raj will have after 7 years with monthly deposits, we need to calculate the future value of an annuity. This involves using the future value of an annuity formula, which accounts for regular deposits and compound interest over time.

Raj wants to determine the total amount of money he will have after 7 years by making monthly deposits of \$500 at an annual interest rate of 10\%. This scenario requires calculating the future value of an annuity.

The future value \( FV \) of an annuity can be calculated using the formula:

\[ FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \]

where:

• \( P \) is the monthly deposit (\$500),
• \( r \) is the monthly interest rate (\( \frac{10}{12 \times 100} = 0.0083333 \)),
• \( n \) is the total number of deposits (7 years \(\times\) 12 months/year = 84 months).

Substituting the values into the formula:

\[ FV = 500 \times \left( \frac{(1 + 0.0083333)^{84} - 1}{0.0083333} \right) \]

Calculating this gives:

\[ FV \approx 60475.2092 \]

Final Answer