If the answer is not an integer, enter it as a decimal rounded to the nearest tenth of a year, if needed.

Question

Suppose $11,400is invested in a monthly compounded account at 4.98%. Approximately how long will it take for the balance to reach $25,650?
If the answer is not an integer, enter it as a decimal rounded to the nearest tenth of a year, if needed.

Answer 1

The formula for compound interest is:

 

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

 

So we want to find t in years and we have all the other variables so we just plug them in

 

25650 = 11400 (1+ (.0498/12))^12t

 

Now we solve for t

 

2.25 = (1.00415)^12t

 

Now we can put them in ln form

 

ln(2.25) = ln (1.00415)^12t

 

We can bring down the exponent

 

ln (2.25) = 12t ln (1.00415)

 

ln (2.25) / ln (1.00415) = 12t

 

195.81 = 12t

 

t = 16.3175 ≈ 16.3 years