Find the time required for an investment of 5000 dollars to grow to 6700 dollars at an interest rate of 7.5 percent per year, compounded quarterly.Your answer is t= how many years?

Answer :

Given:

Final Amount, A = $6700

Principal amount, P = $5000

Interest rate, r = 0.075

Number of compounding periods, n = 4

Required: Number of years

Explanation:

The formula to find the compound interest is

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Substitute the given values.

[tex]\begin{gathered} 6700=5000(1+\frac{0.075}{4})^{4\cdot t} \\ 1.01875^{4\cdot t}=1.34 \\ 4t\ln(1.01875)=\ln(1.34) \\ t=\frac{\ln(1.34)}{4\ln(1.0875)} \\ =0.8723 \end{gathered}[/tex]

Final Answer: t = 0.8723