Final answer:
To determine how much Homer Simpson will have in 20 years, we calculate the future value of his initial $130,000 investment made 9 years ago and the future value of his $2,200 annual investments made at the beginning of each year for 20 years, both at an annual interest rate of 6%.
Step-by-step explanation:
The question involves calculating the future value of an initial investment and a series of annuity payments at a given interest rate. Specifically, we're looking to find out how much Homer Simpson will have in 20 years after investing an initial sum of $130,000 and then continuing to invest an additional $2,200 each year at the beginning of each year for 20 years at an annual interest rate of 6%. This problem can be broken down into two parts: the future value of a lump sum and the future value of an annuity.
First, calculate the future value of the initial $130,000 investment after 29 years (since it was 9 years ago from the start of the new 20-year period). Second, calculate the future value of the series of $2,200 annual payments made at the beginning of each year for 20 years. Both calculations are based on an annual interest rate of 6%, compounded once per year.
To solve the first part, we use the formula for the future value of a lump sum:
Future Value = Present Value × (1 + Interest Rate)^Number of Years
Future Value of the initial investment after 29 years:
$130,000 × (1 + 0.06)^29
To solve the second part, since the payments are made at the beginning of the period, we use the future value of an annuity due formula:
Future Value of Annuity Due = Payment × [((1 + Interest Rate)^Number of Payments - 1) / Interest Rate] × (1 + Interest Rate)
Future Value of the annuity (20 payments of $2,200):
$2,200 × [((1 + 0.06)^20 - 1) / 0.06] × (1 + 0.06)
By calculating both values and adding them together, we obtain Homer's total sum after 20 years. Note that each resulting figure will need to be calculated and then rounded to the nearest cent.