$8,000 placed in account with an annual int. rate of 4.5%, how long will it take to quadruple if the int. is compounded annually?

Question

$8,000 placed in account with an annual int. rate of 4.5%, how long will it take to quadruple if the int. is compounded annually?

 

Answer 1

The formula for compound interest is 

 

A = P*[1 + (r/n)]^n*t      where 

 

P = Principal or initial amount

r = annual interest rate as a decimal

t = number of years

A = Accumulated or final amount

n = number of compoundings per year 

 

Here n = 1, r = 0.045, P = 8000, A = 4*8000 = 32000

 

32000 = 8000*[1 + 0.045]^t

4 = (1.045)^t

 

Take the logarithm of both sides.  You can use any base you want, I prefer the natural logarithm ln (base e), but if you're more comfortable with base 10 logs those will work just as well.  

 

ln4 = ln(1.045^t) = t*ln1.045

t = ln4 / ln1.045 ~ 1.386 / 0.044 = 31.5 years 

 

To check this, raise 1.045 to the 31.5 power and you should get a number very close to 4 (I got 4.001).