Question

8. Find the time required for an investment of 5000 dollars to grow to 7900 dollars at an interest rate of 7.5 percent per year, compounded quarterly.Your answer is t=years.You may enter the exact value or round to 2 decimal places.

Answer 1

Given

Principal = 5000

Amount = 7900

Rate = 7.5%

Find

Time

Step-by-step explanation

we know the formula of comounded quarterly, is given by

`A=P(1+(r)/(400))^(4t)`

now substitute the values,

`\begin{gathered} 7900=5000(1+(7.5)/(400))^(4t) \\ 1.58=(1+0.01875)^(4t) \\ \end{gathered}`

taking ln both sides,

`\begin{gathered} \ln(1.58)=4t\ln(1.01875) \\ 0.457=4t(0.017) \\ t=(0.457)/(4*0.017) \\ \\ t=(0.457)/(0.068) \\ t=6.72 \end{gathered}`

Final Answer

Therefore , t = 6.72 years