A man invests $7000 in an account that pays 6.5% interest per year, compounded semi-annually. Find the amo t after 5 years. How long will it take for the investment to quadruple?

In five years he'll have $9638.26. It'll take approximately 21.7 years to quadruple the investment.

Step-by-step explanation:

In order to solve this problem we need to apply the correct formula for compounded interest that is shown below:

M = C * (1 + r/n) ^ (n*t)

Where M is the final amount, C is the initial amount, r is the interest rate, n is the amount of times it's compounded in a year and t is the time elapsed.

M = 7000 * (1 + 0.065/2) ^ (2*5)

M = 7000 * (1 + 0.0325) ^10

M = 7000 * (1.0325) ^10 = 9638.26

In five years he'll have $9638.26

To quadruple M must be equal to 4*C, since C is 7000, then M is 28000. We have:

28000 = 7000 * (1.0325) ^2*t

(1.0325) ^2*t = 28000/7000

(1.0325) ^2*t = 4

ln[ (1.0325) ^2*t] = ln (4)

2*t*ln (1.0325) = ln (4)

t = ln (4) / [2*ln (1.0325) ] = 21.6723

It'll take approximately 21.7 years to quadruple the investment.