Question

How long will it take for an investment of 1600 dollars to grow to 7500 dollars, if the nominal rate of interest is 7 percent compounded quarterly? FV = PV(1 + r/n)^ nt Answer = ____years. (Be sure to give 4 decimal places of accuracy.)

Answer 1

Investment: $1600

Nominal rate of interest: 7% = 0.07

Composition: Quarterly (n = 4)

Final growth: $7500

Then, using the formula:

$7500=1600(1+\frac{0.07}{4})^{4t}$

Now, solving this equation for t:

$\begin{gathered} 4.6875=1.0175^{4t} \\ 4.6875=1.0175^{4t} \\ \ln (4.6875)=\ln (1.0175^{4t}) \\ \ln (4.6875)=4t\ln (1.0175^{}) \\ t=\frac{\ln (4.6875)}{4\cdot\ln (1.0175^{})} \\ \therefore t=22.2625\text{ years} \end{gathered}$