Suppose you want to have \( \$ 400,000 \) for retirement in 35 years. Your account earns \( 10 \% \) interest. Round answers to the nearest cent. a) How much would you need to deposit in the account each month? b) How much interest will you earn?
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To grow your retirement fund to \( \$400,000 \) in 35 years with an annual interest rate of \( 10\% \), you'll need to deposit a monthly amount into the account. Using the future value of an annuity formula, the monthly deposit needed is approximately \( \$461.63 \). So, just imagine your future self relaxing on a beach, thanks to those little monthly contributions! Now, regarding the interest earned: after 35 years, with the monthly contributions of about \( \$461.63\), you will accumulate around \( \$316,000 \) in interest! That's a neat little bonus on top of your savings, almost as delightful as a surprise party for your future self when retirement finally arrives!