Answer: 262.752692months
The account will take 21.8960577years = (262.75) months to grow to $250,000
Explanation:
Using Compound interest formula
A = p + (1+ r/n)^nt
Note :( ^ ) means raised to the power of
A= amount = $250,000
r = nominal rate = 18% =18/100 =0.18
P = principal = $5,000
n = number of compounded years
=12 ( it means 12 interest payment per year)
t = time in years to grow
250,000 = 5,000 ( 1+0.18/12) ^12(t)
250,000 = 5,000 ( 1 + 0.015)^12t
250,000 = 5,000 (1.015)^12t
Divide both sides by 5,000
1.015^12t = 250,000/5,000
1.015^12t = 50
Take In of both sides
In 1.015^12t = In 50
Using exponential function rule to express the above equation
12t In 1.015 = In 50
12t = In 50 / In 1.015
12t = 3.91202301 / 0.0148886125
12t = 262.752692
t = 262.752692 / 12
t = 21.8960577 years
t = 262.752692 months
