Question

You want to have 2.25 million when you retire in 38 years. You feel that you can save $415 per month until you retire. What annual percentage rate (APR) do you have to earn in order to achieve your goal?

Answer 1

To achieve a retirement goal of $2.25 million in 38 years with monthly savings of $415, you would need to earn an annual percentage rate (APR) of approximately 4.65%.

Step-by-step explanation:

To determine the annual percentage rate (APR) that you need to earn in order to achieve your retirement goal, we can use the formula for compound interest.

Let's break down the information given:

• Retirement goal: $2.25 million
• Years until retirement: 38
• Monthly savings: $415

In order to calculate the APR, we first need to calculate the future value of your monthly savings over 38 years. We can use the compound interest formula:

P(1+r/n)^(n*t)

Where:

• P is the principal amount (your monthly savings)
• r is the annual interest rate
• n is the number of times that interest is compounded per year (12 for monthly savings)
• t is the number of years

Plugging in the values:

415(1+r/12)^(12*38) = 2,250,000

To solve for r, we can use algebraic manipulation:

(1+r/12)^(12*38) = 2,250,000/415

Now, we can use trial and error or a financial calculator to find the value of r that satisfies the equation. In this case, the APR is approximately 4.65%.