How long for an investment to triple?

Question

How long will it take an investment to triple, if the interest rate is 5% compounded annually? Set up and solve an equation that requires the use of logs to solve. Do not use continuous compounding.

Answer 1

You will use the formula

 

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

 

where:

A = accumulated amount

P = investment

t = time

r = interest rate

n = number of times compounded per year

 

P = P

A = 3P   

r = 0.05

n = 1

t = 1

 

Substituting these values into the formula,

 

3P = P(1 + 0.05)^t

 

 

Divide by  P on both sides of equation.

 

3 = 1.05^t

 

 

Log both sides of equation

 

log(3) = log(1.05)^t

 

 

Bring the exponent t down as the coefficient of the log(1.05)

 

log(3) = t log(1.05)

 

 

Divide by log(1.05) on both sides of equation

 

t = log(3) / log(1.05)

t = 22.52

 

 

It will take 22.52 years to triple the investment at interest rate of 5%.