Question

​(Related to Checkpoint​ 6.1) ​ (Future value of an​ annuity)Imagine that Homer Simpson actually invested the $100,000 he earned providing Mr. Burns entertainment 10 years ago at 11.5 percent annual interest and that he starts investing an additional ​$2,500 a year today and at the beginning of each year for 15 years at the same 11.5 percent annual rate. How much money will Homer have 15 years from​ today?

Answer 1

To calculate the future value of an annuity, use the formula FV = P * ((1 + r)^n - 1) / r. For Homer Simpson's investment of $100,000 10 years ago and additional investments of $2,500 per year for 15 years at an 11.5% annual interest rate, the future value is $833,103.32.

Step-by-step explanation:

To calculate the future value of an annuity, we can use the formula:

FV = P imes ((1 + r)^n - 1) / r

Where:

• FV is the future value
• P is the periodic payment
• r is the interest rate per period
• n is the number of periods

In this case, Homer Simpson invested $100,000 10 years ago and is now investing an additional $2,500 at the beginning of each year for 15 years. The interest rate is 11.5% per year.

Using the formula, we can calculate the future value:

FV = 100,000

imes ((1 + 0.115)^10) + (2,500

imes ((1 + 0.115)^15 - 1) / 0.115) = $833,103.32