You are considering investing in a European 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? Round fractional months up.
A) 23
B) 27
C) 32
D) 38
E) 44

Question

Quizplus · Accepted Answer

We can use the formula for compound interest to solve this problem:

A = P(1 + r/n)^(nt)

where:
A = final amount ($250,000)
P = initial investment per month ($5,000)
r = annual interest rate (18%)
n = number of times interest is compounded per year (12 for monthly)
t = time in years (unknown)

Plugging in the given values, we get:

$250,000 = $5,000(1 + 0.18/12)^(12t)

Simplifying, we get:

50 = (1 + 0.015)^12t

log(50) = 12t*log(1.015)

t = log(50)/(12*log(1.015)) = 37.52

Rounding up to the nearest month, we get:

t = 38

Therefore, it would take 38 months for the account to grow to $250,000. 
The correct answer is D.

You Are Considering Investing in a European Bank Account That