How do you do compound interest problems?

Question

mathmale · Answer

Welcome to OpenStudy!
Others and I would love to help you, Lila, but your question is so broad that it'd be hard to know where to start.  Could you please find a specific problem or two on which we could concentrate?  
Could you find and share the formula for the compound interest amount when interest is paid annually, that is, just once per year?  That'd be a good start.

anonymous · Answer

The question is 
Use the compound interest formulas A=P(1+r/n)^nt and Pe^rt to solve the problem given. Round answers to the nearest cent. Find the accumulated value of investment of $15,000 for 6 years at an interest rate of 4% if the money is a. Compounded semiannually  b. Compounded quarterly c. Compounded monthly and d. Compounded continuously 


I have to find all four of those things and I have no clue how to

mathmale · Answer

Let's assume that compounding occurs annually (once per year) as an example.  
In your formula, $$A=P(1+\frac{ r }{ n })^{nt}$$

mathmale · Answer

P=principal=$15,000
r=annual interest rate=4%    which must be rewritten as 0.04
n=number of compounding periods per year = 1
t= number of years  = 6

The Amount after 6  years, with interest compounded annually, would be$$A=$15000(1+\frac{ 0.04 }{ 1 })^{1*6}=$15000(1+0.04)^{6}$$

mathmale · Answer

Calculate that.

Next, assume semi-annual compounding.  Let n=2.  show your work, including your result for the Amount.

anonymous · Answer

Okay so for the first part though is the initial investment always P in the equation?

mathmale · Answer

Yes.  The initial amount of money, which we call the Principal, stays the same.  But all the Amounts differ from one another if you change the number of times per year when interest is compounded.

anonymous · Answer

Okay so the first one was annually so when ever I have one that needs to be done annually that's the way I would set it up?