Interest word problem. How much will it be worth in 8 years?

Question

Suppose you invested $200 at 9% interest, with no withdrawals made.How much will the investment be worth after 8 years, if the interest is compounded monthly.

 

Answer should be in dollars, accurate to the nearest cent.

 

I tried to solve it so I used the formula --> A= P(1+r/100)^n  

I got the answer 398.5125 but I am not sure if it is right.

Answer 1

If the 9% is an annual rate, this is incorrect.

The process you describe works only if the compounding period is the same as the period over which the interest rate is defined

 

In this case, the monthly rate is 9%/12 = 0.75% = 0.0075

and you have 8 years*12months/year = 96 months

 

Therefore, your answer is 200*(1+0.0075)^96 = $409.78