# How to find nominal annual rate of interest/discount?

1) at what nominal annual rate of interest, convertible four times a year will you quadruple your investment in $15$ years?

2) the annual nominal rate of interest compounded quarterly is $i^{(4)} = 0.08$. what is $d^{(2)}$, the equivalent nominal annual rate of discount compounded semiannually?

Sorry in advance, these are homework problems that I just can't get the right answers. for $1)$ I did $(1+i)^{4*15} = 4$ and get $i=0.023$, then did $(1+0.023)^4-1 = 0.0968$ but this is not the right answer. Also for $2)$ what I've done is since we know $1-d = \frac{1}{1+i}$, $(1+\frac{0.08}{4})^2 - 1 = 0.0404$ then i found $d$ to be $0.0388$ both wrong. How do i get the right interest/discount?

• What is the answer for 1)? Are you close so it might be a convention thing? – spaceisdarkgreen Feb 16 '17 at 18:01
• @spaceisdarkgreen i do not know the answer for either one – Allie Feb 16 '17 at 18:02
• Reading the definition of nominal interest rate on wikipedia, I suspect that instead of doing $(1+.023)^4-1$ you should just do $.023*4=.0935$ – spaceisdarkgreen Feb 16 '17 at 18:04

So, for the first one, you correctly get the quarterly interest rate of $i=0.023$ and the answer should just be four times that
For the second, I think you did everything right except you need to double the $d=0.0388,$ since they want the nominal annual discount whereas you computed the semiannual discount.