Question

You have $50,176.72 in a brokerage account, and you plan to deposit an additional $7,000 at the end of every future year until your account totals $400,000. You expect to earn 11.8% annually on the account. How many years will it take to reach your goal? Round your answer to two decimal places.

Answer 1

Present Value in account PV = $50176.72

Amount deposited each year = P = $7000

Future Value required in account = $400000

Interest Rate = r = 11.8% or 0.118

Let the number of years be n

=> FV = PV(1+r)ⁿ + P(1+r)^n-1 + P(1+r)^n-2 +...+ P(1+r)² + P(1+r) + P = PV(1+r)ⁿ + P[(1+r)ⁿ -1]/r

=> 400000 = 50176.72*(1+0.118)ⁿ + 7000[(1+0.118)ⁿ -1]/0.118

=> 400000 = 50176.72*(1+0.118)ⁿ + 59322.033*(1+0.118)ⁿ - 59322.033

=> (1+0.118)ⁿ = 459322.033/109498.753

=> n = ln (459322.033/109498.753) / ln(1.118) = 12.85 years