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

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