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3 years ago

Lucy have $6400 if she invests $1200 at 15% interest compounded quarterly?

Mathematics

1 answer:

svet-max [94.6K]3 years ago

8 0

Answer:

11.4 years

Step-by-step explanation:

We assume you want to know the time it takes for Lucy's investment of $1200 to have a value of $6400. The compound interest formula is good for finding that.

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

for principal P invested at rate r per year for t years, compounded n times per year. We want to find t such that ...

6400 = 1200(1 +0.15/4)^(4t)

16/3 = 1.0375^(4t) . . . . divide by 1200

log(16/3) = 4t·log(1.0375) . . . . take logarithms

t = log(16/3)/(4·log(1.0375)) ≈ 11.4

It will take about 11.4 years for Lucy's investment value to be $6400.

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