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 $280,000? Round fractional months up.

Question

Quizplus · Accepted Answer

We can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
where A is the amount, P is the principal (initial investment), r is the nominal annual rate (18%), n is the number of times compounded in a year (12 for monthly), and t is the time in years.
We want to solve for t, so we can rearrange the formula:
t = (log(A/P))/(n*log(1 + r/n))
Plugging in the given values:
P = 5000 (since this is invested at the beginning of each month)
A = 280000
r = 0.18
n = 12
t = (log(280000/5000))/(12*log(1 + 0.18/12)) ≈ 40.91
Rounding up to the nearest whole number, it will take 41 months to reach $280,000. Therefore, the best choice is B.

You Are Considering an Investment in a Third World Bank