Question

You have $12,013.05 in a brokerage account, and you plan to deposit an additional $3,500 at the end of every year until your account totals $100,000. You expect to earn 12.2 percent annually on the account. How long will it take to reach your goal?

a. 7yrs

b.8yrs

c.6

d.9

e.10

Answer 1

We use the formula:  
A=P(1+r/100)^n
where   
A=future value
P=present value  
r=rate of interest
n=time period.

Future value of 12,013.05=12,013.05*(1.122)^n

Also:

Future value of annuity=Annuity[(1+rate)^time period-1]/rate

=3500[(1.122)^n-1]/0.122

Hence 100,000=12,013.05*(1.122)^n+3500[(1.122)^n-1]/0.122

100,000=12,013.05*(1.122)^n+28688.5246[(1.122)^n-1]

100,000=12,013.05*(1.122)^n+28688.5246*(1.122)^n-28688.5246

(100,000+28688.5246)=(1.122)^n[12,013.05+28688.5246]

(100,000+28688.5246)/(12,013.05+28688.5246)=(1.122)^n

3.16175789=(1.122)^n

Taking log on both sides;

n*log 1.122=log 3.16175789

n=log 3.16175789/log 1.122

=10 years