Question

A sum of $4000 is invested at 5.5% interest per year. Find the amount of time needed to double the money if it’s compounded monthly.

A) 12y
B) 12y 4m
C) 12y 8m
D) 13y

Answer 1

9514 1404 393

Answer:

C) 12y 8m

Explanation:

The amount of principal P at compound monthly at interest rate r per year is given by ...

A = P(1 +r/12)^(12t) . . . . after t years

Here, we want to find t, so ...

A/P = (1 +r/12)^(12t)

log(A/P) = (12t)·log(1 +r/12)

t = log(A/P)/(12·log(1 +r/12))

Filling in the given values, we find t to be ...

t = log(8000/4000)/(12·log(1 +0.055/12)) ≈ 12.6315 ≈ 12 years 7.6 months

It will take about 12 years 8 months to double the money.