Question

Find the time required for an investment of 5000 dollars to grow to 6800 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

The initial investment is given 5000 dollar , interest rate is 7.5 percent per year compounded quarterly.

Required

To determine the time required to grow the initial investment of 5000 dollar to 6800 dollar.

Step-by-step explanation

The formula for the amount ,

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

For compounded quarterly , n=4.

Substitute the values.

`\begin{gathered} 6800=5000(1+(7.5)/(100*4))^(4* t) \\ (68)/(50)=(1+0.01875)^(4t) \\ 1.36=1.01875^(4t) \end{gathered}`

Take ln both sides.

`\begin{gathered} ln1.36=4tln1.01875 \\ 4t=(0.3074)/(0.018576) \\ 4t=16.54 \\ t=4.137 \end{gathered}`Answer

Hence the time required for an investment of 5000 dollars to grow to 6800 dollars at an interest rate of 7.5 percent per year, compounded quarterly is 4.14 years.