You are depositing $1,500 in a retirement account today and expect to earn an averagereturn of 7.5 percent on this money. How much additional income will you earn if youleave the money invested for 45 years instead of just 40 years?
Question
You are depositing $1,500 in a retirement account today and expect to earn an averagereturn of 7.5 percent on this money. How much additional income will you earn if youleave the money invested for 45 years instead of just 40 years?
Solution
To answer this question, we need to use the formula for compound interest, which is:
A = P (1 + r/n) ^ nt
Where: A = the amount of money accumulated after n years, including interest. P = principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = the time the money is invested for in years
In this case, the principal amount (P) is $1,500, the annual interest rate (r) is 7.5 percent or 0.075 (in decimal), and interest is compounded once per year so n = 1.
First, let's calculate how much the investment will be worth after 40 years:
A = 1500 * (1 + 0.075/1) ^ (1*40)
Then, calculate how much the investment will be worth after 45 years:
A = 1500 * (1 + 0.075/1) ^ (1*45)
The additional income earned by leaving the money invested for 45 years instead of 40 years is the difference between these two amounts.
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