Question

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?

Answer 1

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

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.

Answer 2

$9.638.3; 21.67 years

Explanation:

P=principal=$7,000

r=rate=6.5%=0.065

n=2(semiannually)

t=5 years

A=p(1+r/n)^nt

=$7,000(1+0.065/2)^2×5

=$7,000(1+0.0325)^10

=$7,000(1.0325)^10

=$7,000(1.3769)

=$9,638.3

How long will it take for the investment to quadruple

That means 4 times

4×$7000=$28,000

A=p(1+r/n)^nt

$28,000=$7,000(1+0.065/2)^2t

$28,000=$7,000(1+0.0325)^2t

$28,000=$7,000(1.0325)^2t

Divide both sides by $7,000

4=(1.0325)^2t

Take the log10 of both sides

log4=2t × log1.0325

0.60206=2t×0.01389

0.60206=t×2×0.01389

0.60206=0.02778t

t=0.60206/0.02778

t=21.67 years