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Find the time required for an investment of 5000 dollars to grow to 6600 dollars at an interest rate of 7.5percent per year, compounded quarterly.Your answer is t =years.

User Foundling
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2 votes

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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User Marjeta
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