You are considering an investment in a Third World bank account that pays a nominal annual rate of 18%, compounded monthly. If you invest $5,000 at the beginning of each month, how many months would it take for your account to grow to $250,000?

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