Find the time required for an investment of 5000 dollars to grow to 8800 dollars at an interest rate of 7.5 percent per year, compounded quarterly.

Question

Find the time required for an investment of 5000 dollars to grow to 8800 dollars at an interest rate of 7.5 percent per year, compounded quarterly.

I did 8800=5000(1+(0.075)/(4))^((4*t)) and got 7.6 which was wrong, please help and explain

Answer 1

FV = PV(1 + r/n)^nt, PV = $5000, FV = $8800, r = 7.5% = 0.075; n = 4

8800 = 5000(1 + 0.075/4)^4t; t = 1/4(ln(8800/5000)/ln(1 + 0.075/4) = 7.6 years, can be answer 8 years?

You did everything right

Answer 2

If we understand 7.5% as the Annual Percentage Rate

8,880 = 5,000 (1 + 0.075)^t

and we get t = 7.816 years.