An initial deposit of $20,000 grows at an annual rate of 4% for 14 years. Compare the final balances resulting from annual compounding and continuous compounding. (Give your answers correct to the nearest cent.)
Explain Answers please

Question

An initial deposit of $20,000 grows at an annual rate of 4% for 14 years. Compare the final balances resulting from annual compounding and continuous compounding. (Give your answers correct to the nearest cent.) 
Explain Answers please

phi · Answer

Here is the start of some videos that might help you, if you need more info on how to do this stuff http://www.khanacademy.org/finance-economics/core-finance/v/introduction-to-interest

phi · Answer

You need to know some formulas, and how to use them.

For Compound interest, use 
$$ FutureValue= PresentValue \cdot(1+\frac{i}{n})^{nt} $$
where i is the interest rate (as a decimal, e.g. 4% = 0.04)
n is the number of times compounded per year.  With your problem, n=1 (compounded annually means compounded once a year)
t is the number of years.  For your problem, t= 14 years
Your Present Value = 20,000.
So if we plug in the numbers that we know, i= 0.04, n=1, t=14, you must solve
$$ FV= 20000\cdot (1.04)^{14} $$ 
You will need a calculator to do this.

phi · Answer

the formula for continuous compounding is:
$$ FV= PV \cdot e^{i\cdot t} $$ 
where i is the interest rate= 0.04, and t= the years= 14 years

anonymous · Answer

$$
20000. e^{0.04 \times 14}-20000
   (1+0.04)^{14}=379.921
$$