I can't figure out the answer to this one... I know how to solve it, but my 2 calculators are getting different results.

Question

Order the situations from the account that yields the greatest amount to one that yields the least amount.

​Situation A: You invest $500 in an account at a 12% interest rate, compounded monthly, for 12 years.

​Situation B: You invest $500 in an account at a 10% interest rate, compounded quarterly, for 15 years.

​Situation C: You invest $500 in an account at a 15% interest rate, compounded annually, for 10 years.

Answer 1

First identify your formula: A=P(1+(r/n))^nt

A=final amount

P= principle, or your $500

r= rate

n=number of times compounded each year

t= time frame

Then calculate the amount of interest you would receive for each situation.

Lets do A first:

Situation A:

1.     Identify your variables

a)     P= $ 500

b)     r=.12

c)     n=12 (there are 12 months in a year)

d)     t=12 years

2.     Then place your variables into the formula

a)     A=500(1+(.12/12))^12*12

3.     Now solve (if you have trouble getting different answers from a calculator try expanding your work to see what issues you’re getting)

a)     A=500(1+(.12/12))^12*12

b)     A=500(1+(.01))^12*12

c)     A=500(1.01)^12*12

d)     A=500(1.01)¹⁴⁴

e)     A=500(4.190)

f)      A=2095.307

4.     Situation A gives you $2095.30

Situation B:

This time I am just going to set up the formula and start to solve it with you and give an approximate answer, I encourage you to solve this one on your own.

1.     Identify variables

a)     P=$500

b)     r=.10

c)     n=4 (there are 4 quarters in a year)

d)     t=15 years

2.     The formula

a)     A=500(1+.10/4))^4*15

3.     Solve

a)     First step is divide r/n, .4/10

b)     Next step is to add the answer of r/n to 1

c)     Next step is to multiply r and t

d)     Now finish solving the problem

4.     Situation B result: The result is larger than situation A but less than 2500

Situation C:

This time I am just going to help set up formula and give advice on the answer

1.     Identify Variables

a)     P=$500

b)     r=.15

c)     n=1 (just 1 year in a year)

d)     t= 12 years

2.     Plug into the formula

a)     A=500(1+(.15/1))^1*10

3.     Solve

4.     Answer: it is between 2000 and 4000

Ordering them: Place the situation that yields the greatest amount (its A is highest) on top, followed by the second highest, followed by the lowest

Situation A should be in the middle position

Situation _

Situation A

Situation _