Question

Find the time required for an investment of 5000 dollars to grow to 7200 dollars at an interest rate of 7.5 percent per year, compounded quarterly. Your answer is t = _____ years.

Answer 1

4.91 years

Explanation:

`\displaystyle A=P\biggr(1+(r)/(n)\biggr)^(nt)\\\\7200=5000\biggr(1+(0.075)/(4)\biggr)^(4t)\\\\(36)/(25)=1.01875^(4t)\\\\\ln\biggr((36)/(25)\biggr)=4t\ln(1.01875)\\\\t=(\ln\bigr((36)/(25)\bigr))/(4\ln(1.01875))\\\\t\approx4.91`