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
