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

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0 votes

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

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

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

0 votes

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!