Question

You want to be a millionaire when you retire in 40 years.

a.
How much do you have to save each month if you can earn an annual return of 10.5 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

b. How much do you have to save each month if you wait 15 years before you begin your deposits? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
c. How much do you have to save each month if you wait 25 years before you begin your deposits? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

LOOK AT THE EXPLANATION

Step-by-step explanation:

To determine the monthly savings amount needed to earn an annual return of 10.5 percent, we can use the formula for the future value of an ordinary annuity.

a. If you save each month without waiting:

1. First, we need to calculate the monthly interest rate by dividing the annual interest rate of 10.5 percent by 12.

2. Next, let's assume you want to save for a specific period. To keep the calculations consistent, we'll assume a saving period of 1 year.

3. Plugging these values into the formula, we have:

Future Value (FV) = Monthly Savings (PMT) * [(1 + Monthly Interest Rate)^(Number of Months) - 1] / Monthly Interest Rate

4. Since we want to solve for the monthly savings amount (PMT), we rearrange the formula:

PMT = FV * Monthly Interest Rate / [(1 + Monthly Interest Rate)^(Number of Months) - 1]

5. Given that the future value is not specified in the question, we cannot determine the exact monthly savings amount.

b. If you wait 15 years before you begin your deposits:

1. In this scenario, the saving period would be 15 years.

2. Following the same formula, we can calculate the monthly savings amount needed. However, we'll now have a different number of months.

3. Plugging in the values, we get:

PMT = FV * Monthly Interest Rate / [(1 + Monthly Interest Rate)^(Number of Months) - 1]

4. As the future value is not provided, we cannot calculate the exact monthly savings amount.

c. If you wait 25 years before you begin your deposits:

1. Similar to the previous scenario, we'll use a saving period of 25 years.

2. Applying the formula, we get:

PMT = FV * Monthly Interest Rate / [(1 + Monthly Interest Rate)^(Number of Months) - 1]

3. As the future value is not given, we cannot determine the precise monthly savings amount.

In summary, without specifying the future value, we cannot calculate the exact monthly savings amount needed to earn an annual return of 10.5 percent. The monthly savings amount will depend on the desired future value and the saving period.