HOW TO CALCULATE INTEREST RATE FROM ANNUITY FORMULA

Plen’s answer is correct.

However, you can not be required to do this mathematically in the exam. In the exam you can only be required to use the annuity tables ‘backwards’.

The PV = annuity x annuity discount factor

So, 3500 = 500 x the 10 year annuity discount factor

So, the 10 year annuity discount factor must equal 3500/500 = 7.

Now look at the annuity tables. Go to the 10 year row and see which rate of interest gives a factor of 7.

You will see that 7% results in a discount factor of 7.024, and 8% results in a discount factor of 6.710.

The nearest to 7.000 is 7%. (The exact answer will be slightly more than 7%, but in the exam you would only be required to get it to the nearest %)

@plen said:
umm do u know the answer? cus i have arrived to one and i do not know if what i have done is right 😀

so i used some mathematics here and hopefully i have not broken any math rules -_-

this is what i came up with:

n = 10

3500= 500 [ 1- 1/(1+r)^10 / r all i did here was get read of that negative exponent by reciprocal.
3500= 500 [ (1+r)^10 – 1/ (1+r)^10 / r ] what i have done here is i have solved the numerator fraction part by finding L.C.D
3500= 500 [ -1/r ] we cancel out (1+r)^10
hence r = approx -7 and i dont know how to get rid of the minus 😀 If you substitute the r=7 you get approx 3511 well something close though don’t u think 😉

Cheers

the answer is : 7,07 % (7,07282 )

Hi Sir
bit confuse with 3.5 % 5 year interest for reedeemable debt
how to calculate with 3.5% discount rate annuity.
I requested because annuity table not showing 3.5 %. It is only showing in whole number
Regards

If you are wanting for me to answer, then you must ask in the Ask the Tutor Forum. This forum is for students to help each other (and so I don’t look at it very often).

The formula for calculating the annuity factors is shown at the top of the annuity tables that you get given in the exam (and a copy of them is in our free lecture notes).

However it is very unusual in the exam to be asked to discount at an interest rate that is not in the tables. With redeemable debt, it would only be relevant if you were asked to calculate the market value of the debt and the lenders required rate of return was 3.5%.
More commonly in the exam with redeemable debt, you are given the market value and asked to calculate the cost of debt. In that case (as I explain in the free lectures) you calculate the IRR by making two ‘guesses’ as usual, and you would not choose a rate like 3.5% as one of the guesses.

What on earth are you doing this for? You cannot possibly be required to use the formula ‘backwards’ in the Paper F9 exam and so you really are wasting your time.

The most you could be expected to do (and even this is not so likely) is to use the annuity tables backwards. You can calculate the annuity factor (the PV divided by the annual flow). So look along the 10 year row, find the nearest figure to the annuity factor, and see what interest is at the top of the column!!!