Question

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 1

Given:

Final Amount, A = $6700

Principal amount, P = $5000

Interest rate, r = 0.075

Number of compounding periods, n = 4

Required: Number of years

Step-by-step explanation:

The formula to find the compound interest is

`A=P(1+(r)/(n))^(nt)`

Substitute the given values.

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

Final Answer: t = 0.8723