Find the time required for an investment of $5000 to grow to $8000 at an interest rate of 7.5% per year, compounded quarterly.

6.3 years

Step-by-step explanation:

To find the time in years, we will use the Compound interest formula:

        F = P( 1 + i/m)^mn

Where F = future value of investment ($8000); P = Amount invested ($5000); I

i = interest rate (7.5%); m = number of times money is compounded in a year (m = 4 for quarterly) and n = time of investment in years

Substituting;

           8000 = 5000( 1 + 0.075/4)^4n

    Divide both side by 5000 and simplify the bracket on the right hand side;

       8000/5000 = (1.01875)^4n

              1.6 = (1.01875)^4n

Since n is the power, to solve for it we can introduce the natural logarithm   ( ln);

       ln (1.6) = ln (1.01875)^4n

The power can betaken down according to the Laws of logarithms;

     ln (1.6) = 4n x ln(1.01875)

To get n, divide both sides by 4ln (1.01875);

      ln (1.6)/ 4ln(1.01875) = n

  Therefore; n = 6.3 years

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step-by-step explanation:

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