Answer:
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.
