how do you find annual interest on something?

Question

because im doing some of my math corrections and it says: find the annual interest on these amounts at 4% interest compounded quarrterly.

1. $50,000 2. $7,500 3. $3,000

if you can show me how and explain how to do it that would be great thanks :)

Answer 1

There are 4 quarter in a year so (1+0.04/4)^4 * the amount)
or about 1.0406 * the amount

I get 52030.20, 7804.53 , 3121.81

From the source below
P is the principal (the money you start with, your first deposit)
r is the annual rate of interest as a decimal (5% means r = 0.05)

n is the number of years you leave it on deposit

A is how much money you've accumulated after n years, including interest.

If the interest is compounded once a year:

A = P(1 + r)^n

If the interest is compounded q times a year:

A = P(1 + r/q)^nq

Answer 2

OK. So it's annual interest and you're talking about one year, that's the first fact. Also, the 4% annual interest rate is compounded quarterly - which basically means you take a look at what the accrued balace is on a quarterly basis and then continue further accrual in the year on each of those balances. So 4% annual interest compounded quarterly is 1% per quarter (no higher math there, it's just 4%/4 (the number of quarters in a year).

So basically making the above into a formula:

$50K *(1+1%)*(1+1%)*(1+1%)+(1+1%) gives you the accrued balance at the end of the year of $50K at 4% interest, compounded quarterly. Subtract the $50K from that balance and you get the total annual interest accrued.

If they had told you it was 4% compounded monthly, you'd take 4%/12 and multiple the accruing balance against that 4%/12 twelve times to calculate the total accrued interest (plus principal) at the end of the year.

Hope that makes sense.

Answer 3

There are 4 quarters in an year.
So the formula is, I.e^rt, where I is the investment or principal amount, r is the rate of interest, and t is the time perios.
In your case I will do one partially, you use the calculator to get the results.
1)50000xe^0.04x4=58675.54
Now annualising,
I.e^rx1=58675.54
ie; e^r=58675.54/50000=1.174
taking logarithm on both sides,
r.lgo.e=log 1.174, where log e=1
r=log (1.174)=0.1604 or 16.04% annual rate of return.
You can use the same method for 7500 and 3000 principals in 1 and 2 of your question.
Note: Correction, I think I misread your question as 4% compounded quarterly. So it should be I think 1% quarterly which should be substituted intstead of 4%quarterly in the first formula. Then continue as I said and you will get something close to 4% annual rate of return. Method is OK only change in quarterly rates substitution.

Answer 4

equation you are using is a future value calculation!

formula for that is FV = Present Value "50000" x (1 + r).... divide r within the bracket by 4 ( interest compounded quaterly) then multiply the bracket by power 4 .............remember r is your percentage....so would be 0.04

and then say abra kadabra......and theres your answer, if you ever need any more help feel free just to mail me and i will help ya to the best of my abilities..........take it easy!