Question

Peter has opened a retirement investment account and plan to contribute $6,000 at the end of each year to his account for 30 years. He wants to retire when he has $1 million in the account. What expected annual rate of return must earn to have $1 million in his account?

Answer 1

To find the annual rate of return needed for Peter to retire with $1 million, the future value of an annuity formula is used. The specific rate can be calculated with a financial calculator or an Excel function, as it involves an iterative process that is not easily solved by hand.

Step-by-step explanation:

To determine the annual rate of return Peter must earn to have $1 million in his retirement investment account, we can use the future value of an annuity formula:

The formula for the future value of an annuity is FV = Pmt * [((1 + r)^n - 1) / r], where:

• FV is the future value of the annuity (in this case, $1 million).
• Pmt is the annual payment (or contribution, which is $6,000).
• r is the annual interest rate (which we want to find).
• n is the number of periods (here it's 30 years).

In this situation, we have:

• FV = $1,000,000
• Pmt = $6,000
• n = 30

To solve for the rate r, we rearrange the formula and solve it, typically using a financial calculator or a software tool like Excel, as the equation cannot be algebraically rearranged to solve for r in a simple manner. The process entails plugging in the known values and iteratively computing or finding the rate that sets the equation equal to $1,000,000.

Although the manual calculation for r might not be straightforward, financial calculators and spreadsheets have built-in functions to solve for this interest rate. For example, in Excel, the RATE function can be used.