Small business,

## If the revenue increases at 18 percent per year, how many years will it take to double?

# 3 Answers

If revenues increase at 18 percent per year, it will take 4.188 years to double. The formula is

T=ln(2)/ln(1+r)

If you ever want to quickly estimate how long it takes for something to double, you can use the Rule of 72. The rule number in this case 72 is divided by the interest number is this case 18. 72 divided by 18 is 4.

This should be just a simple FV formula FV=PV(1+rt)

If we want our revenue to double than lets just pick some simple FV and PVs

FV=2 and Pv=1 and r=0.18

2=1(1+.18t) then do simple algebra

2/1=(1+.18t)

2=1+.18t

2-1=.18t

1=.18t

1/.18=t

1/.18=5.56

If the revenue increases at 18 percent per year, it will take 5 1/2 years to double.

The formula is A = P(1 + r/n)^{nt}.

A = accumulated amount (amt that you want at the end)

P = Principle amount (beginning amount)

r = interest rate - remember to change the percent into a decimal, ex: 8.5% = 0.085 - move decimal over twice to the left.

n = how often it compounds in a year

t = time measured in years

For this problem, since we want it to double, we can assume A = 2 and P = 1. Since it's yearly, n = 1, r = .18, and t = ?, because we are solving for t.

2 = 1(1 + .18)^t

2 = (1.18)^t (since t is an exponent, we want to change it into log form.

log_{1.18}2 = t

t = 4.1878.

I hope this helps!!

## Comments

Just to clarify to the students the difference in the answers this is assuming compounded interest with the original formula : FV=PV(1+r/n)

^{nt}^{ }where t=ln(2)/ln(1+.18) while mine was based on simple interest.Comment