Help with an interest Rate Question

DylanII

Hey,

Im hoping someone can help me out.

I have an AER of 10.38%

I need to find the nominal interest rate if I were to compound monthly.

So for example if I compound quarterly the nominal rate would be 10%.
(1+0.1/4)^12 = 1.1038 - 1 = .1038 (the AER) with the 0.1 being the nominal rate.

So I need to find X:

(1+X/12)^12=1.1038?

But how do

Michael Collins

Try taking the log (to any base you like) of both sides. The exponent of 12 will turn into a multiplicative factor on the left-hand side.

DylanII

Hey, thanks for your help

I figured it out, so I thought Id post it incase anyone else is ever looking for something similar.

What I done was:

AER = 0.1038

(1+r/12)^12 = AER + 1

(1+r/12)^12 = 1.103812891 both sides of the equation to the power of 1/12

(1+r/12) = 1.0082648 then multiply both sides by 12

(12+r) = 12.0991776
r= 12.0991776 - 12
r= .0991776
R = 9.91776%

Michael Collins

Yep, that's the way to do it. Taking the log would be no help at all, I wasn't thinking when I posted the above! Sorry!

DylanII

Michael Collins wrote: »

Yep, that's the way to do it. Taking the log would be no help at all, I wasn't thinking when I posted the above! Sorry!

Thanks anyway

Im not the best at math so I just assumed that you had another way of doing it :P

Yakuza

Fair play for sorting it out, here's what I'd have done to make the calcs a little quicker:
You arrived at:
(1+r/12) = 1.0082648
If you subtract 1 from both sides, you get :
r/12 = .0082648 , now multiply both sides by 12 and you get :
r= 0.0991776

Powers / roots are the easiest way to solve such equations