find the amount of money in the bank account given the following conditions:
initial deposit= $5000, annual rate= 3%, time= 2 years

- anonymous

- katieb

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- anonymous

http://d.pr/IASx

- anonymous

a = initial deposit, r = 1.03, n = 2

- waheguru

What grade?

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## More answers

- anonymous

11th

- anonymous

says answer is
5,304.50

- anonymous

It should be 5000 * (1.03)^2. Assuming compounding of the interest rate.

- anonymous

oh so its 5000(1.03)^2

- waheguru

Gt where dide u get the 1.3 from

- anonymous

At the end of first year, you will have: 5000 + 5000 * 0.03 = 5000 * (1.03).
At the end of second year, you will have: 5000 * (1.03) + 5000 * (1.03) * (0.03)
Because you earn interest in the second year on the interest amount of the first year.
So, that is same as:
5000 * (1.03)^2.
In general, for compounded interest, for n years at rate r and principal p, you get:
p * (1+r)^n

- anonymous

oh yeah compounding of interest...
didnt tought of that

- waheguru

OH

- waheguru

I GET IT NOW GT TANKS

- anonymous

so how do i get the answer

- anonymous

Use a calculator to find:
5000 * (1.03) * (1.03).
That should give you: 5,304.50

- anonymous

yup its correct sir

- anonymous

thanks
it swas 5304.5

- anonymous

Sometimes, these kind of problems can be formulated such that the interest rate "r" is compounded semi-annually or something else. In that case, the "formula" will be similar, but in that case, in p*(1+r)^n, r represents the rate of interest for that period (semi-annually for example) and n represents the total "compounding" periods.

- anonymous

well we all stupidly used simple interest formula..silly me

- anonymous

so what is the p r and n represent in the equation

- anonymous

For example, in this exact same problem, if compounding happened semi-annually, then you will have the following at the end of two years:
5000 * (1+0.015)^4

- anonymous

p is initial amount.
n is number of periods.

- anonymous

r is rate of interest for that period.

- anonymous

principle,rate of interest and time period

- anonymous

so if it were 3000 instead of 5000 and rate was 5.5 and time was 5 years how do i set that up

- anonymous

3000 * (1.055)^5

- anonymous

use the same algorithm

- anonymous

assuming annual compounding.

- anonymous

ok so its similar to the other one

- anonymous

correct.

- anonymous

i got 3920.88

- anonymous

rounded

- anonymous

Sounds right.

- anonymous

did i do it right?

- anonymous

Yeah, I got the same. :)

- anonymous

hmm i guess so..

- anonymous

Oh sorry. My mistake. I gave you the sum formula for geometric progression. The correct formula in this case is:
\[a _{n} = ar ^{n-1}\], but in this case, you would take it as \[a _{n} = ar ^{n}\]

- anonymous

so i did it right :D

- anonymous

yes!!

- anonymous

thakns again everyone

- anonymous

say that to GT

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