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- anonymous

Stacey currently has an account balance of $1,007.78. Her initial deposit on the account was $616 and it earned 5.3% simple interest. How long has Stacey held the account?

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- anonymous

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- anonymous

I need help with this question! please help me out i really need to pass this class and Im completely lost in it

- anonymous

i used to know how to solve this, but it's been awhile since I've done these kind of problems.

- anonymous

*kinds

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- mathstudent55

Simple interest is calculated as I = Prt, where P is the principal (amount of money invested), r = rate of interest written as decimal, and t = time
The amount started as P and incresed by Prt, so
P + Prt = 1007.78
616 + (616)(0.053)t = 1007.78
Now you need to solve for t:
Subtract 616 from both sides and simplify:
32.648t = 391.78
Divide both sides by 32.648:
t = 12
Answer: 12 years

- anonymous

can you help me out with this one Liam owns a business earning $43,200 in profits. These profits are appreciating at about 1.2% each year. What are Liamâ€™s profits after six years?

- mathstudent55

In this case, this is not simple interest. His business earns $43,200 Now.
After one year, Liam will earn $43,200 + 1.2% of $43,200. That is
43,200 + 0.012 * 43,200 = 43,200 + 518.40 = 43,718.40
For the next year, year two, he earns 1.2% more than 43,718.40. That is:
43,718 + 1.2% of $43,718.40 =
43,718.40 + 0.012 * 43,718.40 = 43,718.40 + 524.62 = 44,243.02
Every year, he earns 1.2% more than he earned the previous year. This is compound interest. We could continue calculating it year by year for 6 years, but there is a formula for compound interest.
A = P(1 + r/n)^nt
where
A = total value after adding interest
P = original principal value
r = interest rate in decimal
n = number of times interest is compounded in one year
t = number of yerars
In this case we are looking for A, and we have
P = $43,200
r = 0.012
n = 1
t = 6
A = $43,200(1 + 0.012/1)^(1*6)
A = $43,200(1.012)^6
A = $43,200(1.074195)
A = $46,405.22

- anonymous

THANK THANK THANK you you you!!!!!!! YOUR THE BEST EVER!!!!!!!!

- mathstudent55

You're welcome. You're not so bad yourself. :-)
Now go over these problems and try to understand why one is simple interest and the other one is compound interest. The first one, of course, it states that it is simple interest. Try to understand why the second one is compound interest without having been told so.

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