Problem 5-5 Time to reach a financial goal You have $34,605.72 in a brokerage ac
ID: 2743321 • Letter: P
Question
Problem 5-5
Time to reach a financial goal
You have $34,605.72 in a brokerage account, and you plan to deposit an additional $4,000 at the end of every future year until your account totals $220,000. You expect to earn 13% annually on the account. How many years will it take to reach your goal? Round your answer to two decimal places at the end of the calculations.
years
Explanation / Answer
Amount $ Present value 34605.72 Future value required 220000 Apreciation required 185394.3 $185394.3 is the future value of investment of $4000 per year @13% at n years so 185394.3=4000x(1+0.13)^n => 1.13^n= 185394.3/4000 => 1.13^n= 46.349 By applying log => Log(1.13^n) =Log46.349 => n Log1.13 = Log46.349 => n = Log46.349/Log1.13 => n = 1.666/0.053707 => n = 31.39 Time required is 31.39 years