# Finding effective interest rate without principal amount

Dreamworx

I just took a math test and one question asked me to find the "effective interest rate" of an account compounded quarterly at 4.25%. I wrote my teacher a note saying "trick question silly, I need a principal amount to do this ;)" and then wrote what it would be in theory if P was 1. Think I got 1.05 or 105%.

Did I do this right?

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You don't need the principal to know the interest rate

PackManBrainlure

dammit
how do I find rate without principal? He gives partial credit so if I did the 105% right I may be in the clear

eGremlin

If you had just made the principal amount a variable you would have found the answer. Always assume that information not given to you is a variable.

FastChef

account compounded quarterly at 4.25%
is this rate yearly?

Spazyfool

Quarterly is 1/4 of a year.

MPmaster

It's not like it was an equation, I set it to X originally and didn't know what to do with my graphing calculator from there. What should I have done?

Evil_kitten

yeah that's how frequently it's compounded, but is the nominal rate on an yearly base? also should the effective interest rate be expressed on a yearly base as well? if it's not specified i'm going to assume they both are. finally how did you get 105% out of the data given to you?

hairygrape

It's 18.1%

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Gigastrength

YOU are 18,1%.

Snarelure

This board is 18+

Sharpcharm

This.

Also, fuck economics for using a term like effective interest implying a yearly duration.

Just make everything a rate and people would still get the question wrong

TurtleCat

The post you quoted is wrong

TechHater

Starting balance: 1.00
Balance after first quarter: 1.0425
2nd:1.0425^2
3rd: 1.0425^3
4th:1.0425^4 = 1.1811....
What is the definition of effective interest if it's not this?

CodeBuns
King_Martha

Literally the same as what I posted.
t = 1
n = 4

I think it's funny finance yards have to have a formula for every basic word problem they come across.

Spamalot

The quarterly rate is 1/4th of 4.25% or 1.0625%
Since that a percentage, we divide by 100 to get 0.010625
If you started with a dollar (the amount is arbitrary) after 3 months you have 1.010625 dollars.
Your balance increases by the same fraction every 3 months.
After a year you have 1.010625^4 = 1.043182154 dollars.
The effective interest rate is your gain, converted back into a percentage.
4.3182154 percent

That is, you'd have the same money in the bank if they only compounded yearly at 4.3182154 percent. Hence, "effective rate".

If you know where I can get 18 percent FDIC insured, please tell me so I can open an account there!

(Actually, given today's rates, I'd happily settle for 4.25% annually.)

Flameblow

It's funny you still get the result wrong despite the babby formula

WebTool

Doesn't have to be realistic. But the lack of proper grammar is astounding. It literally reads as 4.25 per quarter, not per year.

LuckyDusty

I know. I was in a waiting room last week and a "basics of investing" video was playing in the background.
The numbers really showed how old the presentation was.

I commented because 18% is so unreasonable.
People who "plug & chug" (punch numbers into a formula. Accept whatever comes out.) aren't getting an education at all. A chimp could do that.
You're supposed to learn to think!

BlogWobbles

the rate you actual nignog
put x for the principle and then find the rate

Emberfire

financeformulas.net/Loan_Payment_Formula.html
$P = \dfrac{r \cdot PV}{1 - (1+r)^{-n}}$