Assume that Ray is 38 years old and has 27 years for saving until he retires.He expects an APR of 7.5% on his investments.How much does he need to save if he puts money away annually in equal end-of-the-year amounts to achieve a future value of $1,200,000 dollars in 27 years' time?
A)$44,444.44
B)$20,670.97
C)$14,882.44
D)$13,844.13

Question

Quizplus · Accepted Answer

To find the annual savings amount needed to reach a future value of $1,200,000 in 27 years with a 7.5% annual interest rate, we use the future value of an annuity formula: $FV = P \times \left(\frac{(1 + r)^n - 1}{r}\right)$, where FV is the future value, P is the annual payment, r is the annual interest rate, and n is the number of years. Rearranging the formula to solve for P gives us $P = \frac{FV}{\left(\frac{(1 + r)^n - 1}{r}\right)}$. Plugging in the values ($FV = 1,200,000$, $r = 0.075$, $n = 27$) gives us $P = \frac{1,200,000}{\left(\frac{(1 + 0.075)^{27} - 1}{0.075}\right)}$, which calculates to approximately $14,882.44.

Assume That Ray Is 38 Years Old and Has 27