Fractional part of Compound Interest

[meager basin]

Here is the problem:

The compound amount for a fractional part of a year is defined by the usual formula S = P(1+r)^n, in which fractional values of n are permissible. Find the compound amount of $100 at 4% (Compounded annually) for (a) 6 months, (b) 3 months, (c) 1 month

Solution (Please check)

the Accumulated value for a year is $104

I multiplied the interest ($4) with the quarter of the year

(a)
$100 + $4 * (6/12) = $102
$100 + $2 = $102

(b)
$100 + $4 * (3/12) = $101
$100 + $1 = $101

(c)
$100 + $4 * (1/12) = $100.33
$100 + $0.33 = $100.33

Is my solution correct? Thanks!

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[winter agate]

Guts
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[meager basin]

am I correct?

[crude fog]

No. Exponential functions don't work like that. They grow more as x (or in this case n) increases.

You literally cited the formula and then did something completely different. I don't understand why that happened.

[meager basin]

here is my solution

[crude fog]

...I know. You asked the question "is it correct", to which the answer is "no".

Frankly, I'm not even sure at this point that you've communicated the problem correctly. Can I see a screenshot?

[crude fog]

Why would it matter to note "fractional values of n are permissible"?

[meager basin]

Is this correct?

[crude fog]

No.

[crude fog]

Well, so far as I can tell the left side is, but the right side isn't.

[meager basin]

That is the calculator output

can you check on yours

[crude fog]

Then you plugged it into the calculator wrong.

[crude fog]

That doesn't look like a calculator. That looks like a chatbot.

[meager basin]

Then plug it to yours

[crude fog]

...do you see the difference?

[crude fog]

I did. Ages ago. That's how I know.

[meager basin]

There is no difference

[crude fog]

...yes, check the other two.

[meager basin]

I already did at the calculator

now, can you tell me if I am right or wrong?

[crude fog]

Look at what you wrote.

[crude fog]

Look at this.

[meager basin]

forget it...

[crude fog]

You added one.

[meager basin]

1 + 0.04 = 1.04

[crude fog]

On the right. You added one.

[meager basin]

they're the same

[meager basin]

the calculator and the computer result are the same

[crude fog]

What you wrote is not the same.

[crude fog]

This is not the same. This is wrong.

[meager basin]

ok I get it was a typo

there

[meager basin]

Is this correct?

yes or no?

[crude fog]

I think so.

[meager basin]

Thank you

[meager basin]

+close