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

Answer: 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