you deposit $40 000 into a retirement account at the age of 20, earning an average of 8% annual interest. How much will you have at the age of 65?

Question

Please help

Answer 1

The formula for compound interest is  

 

A = P*(1 + r/n)^nt  where 

 

A = Accumulated or final amount

P = Principal or original amount ($40000) 

r = interest rate as a decimal (0.08) 

n = number of compoundings per year 

t = number of years (65 - 20 = 45)  

 

You don't specify how often the interest is compounded, but if it is once per year then n = 1 and  

 

A = 40000*(1 + 0.08)⁴⁵  

   = 40000*(1.08)⁴⁵ 

   = 40000*31.92044939

   = $1276817.98  

 

If you have a different value for n you can just plug it into the formula.  

 

By the way, if the interest is compounded continuously you would use a slightly different formula (A = Pe^rt) which is why it is very important to specify how often the interest is compounded in problems like this.