i want to calculate the annual effective interest rate given 10% per annum convertible quartely? question 9 Nov 2016 exam

Question

 Question 9 please. I just want to know whats the effective interest rate of the given 10%.

Answer 1

 If you want the effective yearly of the 10% convertible quartely just use the standard conversion formula however if you're looking for the effective yearly interest rate of the investment this is bow you go about it

We first have to work how long it takes for the accumulated value FV>100000

$$70000(1+T\times1.25\% )=100000\implies T=34.2857$$

Therefore T=35 is the smallest value such that FV>100000

$$FV=70000\left(1+35\times 1.25\%\right)\left(1+\frac{10\%}{4}\right)^{\frac{120-35}{3}}=202557.6949$$

$$70000(1+i)^{10}=202557.6949\implies i=11.21031493\%$$

Comments

Thank you. i was confused because the memo said otherwise but thats what i got

Answer 2

Since it's convertible quarterly, we know that it's a nominal amount - let's call it \(i^{(4)}\). Thus, to make it effective quarterly we have to take \(\frac{i^{(4)}}{4}\).

So now we have an effective quarterly rate and to convert it to effective annual we use \(\left(1+\frac{i^{(4)}}{4}\right)^4 =1+i\)

I think this is what you're looking for!

Comments

thank you very much