AuthorTopic: Effective Annual interest Rate
xshorty419x
@2008-11-16 19:03:51
ok help me solve:

It says An investment of \$4000 will grow to \$6520 in 4 years with monthly compounding, the effective annual interest rate will be closest to: (I said it's 12.28%, but that's wrong and it should be 12.29%) How do you get this?!?!
lavalyn
@2008-11-17 16:50:20
You are correct, it's 12.28%. 12.277% is closer.

((6520/4000)^(1/60)-1)*12 = 12.27769%
YusufZiya
@2009-03-27 02:48:44
Hi everybody,
I think the solution is incorrect, because it gives the APR (Annual Percentage Rate) not the Effective Annual Rate. And also its APR is incorrect because it assumes 5 years (5*12=60 months) period, however question says 4 years (4*12=48 months) period.
My solution is here, if you want I can send it in excel format to you e-mail.
4000*(1+r)^(4*12)=6520
(6520/4000)^(1/48)-1
(1+(6520/4000)^(1/48)-1)^12-1

If you copy and paste the second and third lines to an excel sheet, you find 1.023% and 12.99% respectively. The second line is equal to 1.023% which is effective periodic (monthly) rate. If you annualize this effective periodic rate via compounding it (the third line), you can get the EAR (Effective Annual Rate, or Effective Annual Interest Rate (1+1.023%)^12-1), which is equal to 12.99% (but not equal to 12.29% as you said - I think it must be 12.99%)
And also you can get APR (Annual Percentage Rate), which is equal to effective periodic (monthly) rate * Number of period (month) in a year, which is equal to 12.28%. You can reach this figure multiplying the effective periodic (monthly) rate (1.023%) with # of periods in a year (12Months), which is (1.023%*12).