Calculating Annual Effective Interest Rate for Financial Mathematics

[playboy]

How do you find the annual effective rate of interest?
The question reads: You lend a friend $15 000 to be amortized by semiannual payments for 8 years, with interest at j2 = 9%. You deposit each payment in an account paying J12 = 7%. What annual effective rate of interest have you earned over the entire 8-year period?
Ans = 8.17%
Hmmm... i have absolutly no idea how to get the annuale effective rate of interest.
My TA showed, (in another question) that its something like (1 + i)^n = 1 + r
and solve for r?
Please help somebody
Thanks

 

[hotvette]

Conceptually, it works like this. There is initial outlay of $15,000. The payments that come in annually are immediately invested. At the end of 8 years there is a total value of all investments. The 'effective' interest rate is the equivalent rate at which the initial outlay would compound at to achieve the same final result after 8 years. It might help to draw out a time line and treat each pmt and ensuing investment as a separate problem. Find out how much each is worth after the 8 years is up, sum the totals together, and then it's a straightforward back solution for a std compound interest problem.

By the way, you have 2 identical posts. If this was intentional, pls avoid that in the future.

P.S. One of the most useful classes (in terms of constantly using the material learned) I took in graduate school was called "Engineering Economy".

 

[playboy]

No, that was not intentional, i didn't know i did that :S... I will avoid that in the future!