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