Answer:
3.74 years
Explanation:
You want to know the time it takes for $5000 invested at 7.5% compounded quarterly to grow to $6600.
Compound interest
The amount in an account earning compound interest is ...
A = P(1 +r/n)^(nt)
Principal P invested at annual rate r compounded n times per year for t years.
Time
Solving for t, we have ...
A/P = (1 +r/n)^(nt)
log(A/P) = nt·log(1 +r/n)
t = log(A/P)/(n·log(1 +r/n))
For the given values, this becomes ...
t = log(6600/5000)/(4·log(1 +0.075/4)) ≈ 3.736
The time required for the investment to grow is about 3.74 years.
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