High School

You plan to invest in securities that pay 9.7%, compounded annually. If you invest $5,000 today, how many years will it take for your investment to grow to $7,242.60?

A. 4.00 years
B. 7.82 years
C. 8.00 years
D. 3.63 years
E. 10.31 years

Answer :

It will take approximately- D. 3.63 years for the investment to grow to $7,242.60.

How to find?

Given that the interest rate is 9.7% compounded annually, the initial investment is $5,000 and the final value is $7,242.60.

We need to find how many years it will take for the investment to grow to $7,242.60. We can use the following formula to solve for time:T = log(PV/FV) / log(1 + r)where, T is the time in years, PV is the present value, FV is the future value, r is the annual interest rate (as a decimal).

The values for the given variables are as follows: PV = $5,000FV = $7,242.60r = 9.7% or 0.097Substituting these values in the above formula, we get: T = log(5000/7242.60) / log(1 + 0.097)T ≈ 3.63 years.

Therefore, it will take approximately 3.63 years for the investment to grow to $7,242.60.

Option (d) 3.63 years is the correct answer.

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