Question

You have $7,115.21 in a brokerage account, and you plan to deposit an additional $5,000 at the end of every future year until your account totals $270,000. You expect to earn 14% 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.

Answer 1

Future Value = $ 270000

Rate of Interest = 14% Annually

Annual Instalment = $ 5000

$ 270000 Consists of two parts. One amount is $ 7115.21 growing annually at the rate of 14% p.a and another amount is future value of annual Contributions of $ 5000 Every year

We know that

Future value of Ordinary Annuity = P*[( 1+i)^n-1]/i

Here P = Payment amount

i= Rate of interest

n = No.of Payments.

$ 270000= $ 7115.21( 1+i)^n+ $ 5000[ ( 1+0.14)^n-1]/0.14

$ 270000= $ 7115.21( 1.14)^n +$ 5000[ (1.14)^n-1]/0.14

$ 270000*0.14 = $ 7115.21[ ( 1.14)^n + $ 5000[ ( 1.14)^n - 1]

$ 37800 = $ 7115.21( 1.14)^n + $ 5000( 1.14)^n - $ 5000

$ 37800+$ 5000 = ( 1.14)^n[ $ 7115.21+$ 5000]

$ 42800= ( 1.14)^n [ $ 12115.21]

$ 42800/$ 12115.21 = ( 1.14)^n

3.5327 = ( 1.14)^n

Applying logarithms on both sides

Log 3.5327 = Log ( 1.14)^n

log 3.5327 = n log 1.14

0.5481 = n 0.0569

n = 9.63 Years

Hence it will take around 9.63 years to reach $ 270000.