One has deposited money into a bank account that earned 1.25% simple interest each year. After 12 year, he had earned $5.00 in interest on the account.

If no other money was deposited into or withdrawn from the account, how much was his initial deposit?

Question

One has deposited money into a bank account that earned 1.25% simple interest each year. After 12 year, he had earned $5.00 in interest on the account.

If no other money was deposited into or withdrawn from the account, how much was his initial deposit?

3mar · Answer

@mathmate 
If you could help, I would be grateful!

queenbb · Answer

i need heelp

mathmate · Answer

The formula for simple interest is
I=Pin
where 
I=acumulated interest
P=principal
i=annual interest (in decimal form)
n=number of years.
So putting numbers in,
5.0=P(0.0125)12
Solve for P.

3mar · Answer

Thank you for good explanation, @mathmate !!
It really shows up it!

3mar · Answer

But it shows a decay and I think it is a growth!
am I right, @mathmate?

mathmate · Answer

The question says 
1. simple interest, so it is NOT an exponential growth (or decay), it means that interest for a given principal will accumulate the same interest year after year, there is no compounding, that is why
I=Pin
2. The given amount is the interest, principal is not included, that is why the principal is much higher (6-7 times) than the interest over 12 months.

mathmate · Answer

The formula for combined principal and interest would therefore be:
Accumulated amount=P+I=P+Pin=P(1+in)

will.h · Answer

We can use the formula
A = P(1 + r)^x

Since A is 5 and r is 1.25% and x is 12 years
5 = P(1 + 0.0125)^12

5 = p(1.0125)^12
5 = p(1.160754518)
4.307543002 = p

So the initial investment is 4.307543002

The question is does it even worth to wait all that for such investment xD

3mar · Answer

"2. The given amount is the interest, principal is not included, that is why the principal is much higher (6-7 times) than the interest over 12 months."????
@mathmate

mathmate · Answer

Recall that we are working with 1.25% $simple$ interest, even though this has disappeared from the market for years since computer age. FYI: http://www.investopedia.com/terms/s/simple_interest.asp P is principal, so solving for P, we have 5=P(0.0125)(12) P=5/(12/0.0125)=$33.33

3mar · Answer

Do you mean
$$P=5/(12/0.0125)=$33.33$$
or 
$$P=5/(12*0.0125)=$33.33$$??

mathmate · Answer

Sorry, the latter!
I was rationalizing 0.0125 as 1/80 and dividing 12 by 80.

3mar · Answer

so is it *  or   /  ?

mathmate · Answer

$P=5/(12*0.0125)=$33.33$
is correct as the result of solving
I=Pin => P=I/(in)

3mar · Answer

Oooooooh so the simple interest imply that it is just the amount of bulk × annual interest  and that is for one year.

If it is calculated for n years, it would be      P×i×n

I GOT IT!

I am so much thankful to you!

mathmate · Answer

No problem!   :)