Question

You want to be a millionaire when you retire in 45 years. a. How much do you have to save each month if you can earn an APR of 11.1 percent? (Do not round intermediate calculations and round your answer

Answer 1

To become a millionaire in 45 years with an APR of 11.1%, one would have to determine the monthly savings needed using the future value of an annuity formula, considering the conversion of annual rate to a monthly rate and the total number of payments.

Step-by-step explanation:

To achieve the goal of becoming a millionaire upon retirement in 45 years with an Annual Percentage Rate (APR) of 11.1%, one needs to determine how much should be saved each month. This involves using the formula for the future value of an annuity:

`FV = P × {[(1 + r)^n - 1] / r}`
Where:

• FV is the future value of the annuity (how much you want to have in the future, which is $1,000,000).
• P is the payment amount per period (monthly savings needed).
• r is the interest rate per period (11.1% annual rate converted to a monthly rate).
• n is the total number of payments (total months in 45 years).

First, we need to convert the annual interest rate to a monthly rate by dividing by 12:
r = 11.1% / 12 = 0.925% per month

Then, we calculate the total number of payments for 45 years:

n = 45 years × 12 months/year = 540 months

We rearrange the formula to solve for P:

`P = FV / {[(1 + r)^n - 1] / r}`

Substituting FV = $1,000,000, r = 0.00925, and n = 540:

`P = $1,000,000 / {[(1 + 0.00925)^540 - 1] / 0.00925}`

After calculating the above formula, we find out how much needs to be saved each month to become a millionaire. Starting early and leveraging the power of compound interest can increase the savings significantly over time.