math alebra 1 help

Question

Bernie deposited 

$

2,000

 in an account earning 10% interest compounded annually.

To the nearest cent, how much will he have in 5 years?

Answer 1

The equation for simple interest is:

A = P(1+rt);

A - final amount

P - initial, principal balance

r - annual interest rate

t = time in years.

A = 2000(1+.10*5) = 3000.

Answer 2

A = 2,000(1+.10)^5

= 2000(1.1)^5

= $3,221.02

the general formula is

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

A= ending Amount

P=starting Position

r = annual rate of interest

n= number of compounding periods per year

t = time, in years

t=5, n=1, r=10% = .10

P=2000

had the problem asked for simple interest, instead of compounding

then there would have been 10% of 2000 = 200 per year

200 x 5 = 1000, so A=3000, but his problem requires

annual compounding so

A= 2000(1.1)^5

you need a calculator

or some tedious long hand multiplication

A=2000(1.1x1.1x1.1x1.1x1.1x1.1)

= 2000(1.61051)

= 3221.02

with simple interest, you only get interest on the original amount

with compounding interest, you get interest on the interest

in this case, it comes to exactly $3,221.02

no rounding is needed. that's the exact Amount, to the penny

had the problem asked for continous compounding

the formula would have become

A= Pe^rt = 2000e^(.10x5) = 2000e^.5 = 3297.44

that's useful as a rough check on the answer, as any compounding less than

continous will have an ending Amount less than for continous compounding