Calculating Annual Effective Rate of Interest: A Comprehensive Guide

[playboy]

Hod 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

 

[Fermat]

The lender has invested $15 000 over an 8-year period. What will his $15 000 have become at the end of the 8 years ?

Do you know how to calculate the Return on a Principle sum earning interest at r% pa over a term of n years ?
In your lender's case, $15 000 is the Principle, you have yet to work out the Return, n is 8 years, and r would be the annual effective rate of interest that you have to find.

The first part is a simple repayment scheme.
A borrower gets a loan of $15 000 to be repaid in 16 semi-annual instalments.
The annual rate for the loan is 9%. What is his repayment every six months ?
Have you done loan repaymant schemes ?

The 2nd part is the actual (rather than the effective) investment.
The lender receives R (the borrrower's six-monthly repayment value) every 6 months and immediately puts it into an account earning 7% annual interest.
He does this for 8 years. How much money (the Return) willl be in the account at the end of that time ?

Now that you have found the Return, you can work out the effective annual interest rate.

 

[hotvette]

There were 2 identical posts. I replied as well.

https://www.physicsforums.com/showthread.php?t=99212

 

[Fermat]

Ah, thanks. Didn't notice that post.
Seems our op wasn't too sure which forum his query should go in, so opted to use both of 'em

btw, in your post, you mention "The payments that come in annually ..."
Those payments should be semi-annual.