How many years would it take for Jughead to save an adequate amount for retirement if he deposits $2,000 per month into an account beginning today that pays 12 percent per year if he wishes to have a total of $1,000,000 at retirement?
A) 13.7 years
B) 15.5 years
C) 14.9 years
D) 11.5 years

Question

Quizplus · Accepted Answer

We can use the formula for future value of an annuity to solve this problem:

FV = PMT x (((1 + r)^n - 1) / r)

Where:
PMT = $2,000 (monthly deposit)
r = 12%/12 = 1% (monthly interest rate)
n = number of months

We want to find n, so we can rearrange the formula as follows:

n = ln(FV x r / PMT + 1) / ln(1 + r)

Plugging in the values, we get:

n = ln($1,000,000 x 0.01 / $2,000 + 1) / ln(1.01)
n ≈ 178.93 months

To convert months to years, we divide by 12:

n ≈ 14.91 years

Therefore, it would take Jughead about 14.9 years to save an adequate amount for retirement if he deposits $2,000 per month into an account beginning today that pays 12 percent per year if he wishes to have a total of $1,000,000 at retirement.

How Many Years Would It Take for Jughead to Save