If you want to save $1 000 000 for retirement with $200 monthly deposits at eight percent interest compounded monthly,how long will it take?

Question

Quizplus · Accepted Answer

Using the formula for compound interest, we have:
FV = PV(1 + r/n)^(nt) where FV is the future value, PV is the present value, r is the interest rate, n is the number of times compounded per year, and t is the time in years.

Plugging in the given values, we have:
1 000 000 = 200(1 + 0.08/12)^(12t)
5 000 = (1 + 0.08/12)^(12t)

Taking the natural logarithm of both sides, we have:
ln(5 000) = 12t ln(1 + 0.08/12)
t = ln(5 000)/(12 ln(1 + 0.08/12)) ≈ 44.33

Rounding to the nearest month, we get 44 years and 4 months, which is answer choice C.

If You Want to Save $1 000 000 for Retirement