Question

Starling wants to retire with $3180000 in his retirement account

exactly 27 years from today. He will make annual deposits at the
end of each year to fund his retirement account. If he can earn 8
percent per year, how much must be deposited each year?

Answer 1

The problem deals with finding the annual deposit needed to retire with $3,180,000 in 27 years, given an 8% annual interest rate, using the future value annuity formula.

Step-by-step explanation:

The student is asking how much must be deposited each year to have $3,180,000 in a retirement account after 27 years with an annual interest rate of 8%. This is a financial mathematics problem related to the future value of an annuity. To solve it, we use the future value annuity formula:

FV = P × { [(1 + r)n - 1] / r }

Where FV is the future value, P is the annual deposit, r is the annual interest rate, and n is the number of years. Rearranging the formula to solve for P, and plugging in FV = $3,180,000, r = 0.08, and n = 27, we can calculate the annual deposit required. For this problem, one must use financial calculators or software to get the answer, as the equation involves finding the value for P that satisfies the future value equation for an annuity. Compound interest is a critical concept in retirement planning, as it determines how investments grow over time. Making regular deposits into a retirement account and allowing those funds to grow through compound interest can lead to a substantial amount at retirement, as illustrated in the given examples.