Calculating Annual Effective Rate of Interest: A Comprehensive Guide

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Homework Help Overview

The discussion revolves around calculating the annual effective rate of interest in a scenario involving a loan of $15,000, amortized through semiannual payments over 8 years at an interest rate of j2 = 9%. The original poster expresses uncertainty about how to determine the annual effective rate earned from these transactions, particularly after depositing payments into an account with J12 = 7% interest.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between the loan repayment scheme and the investment return, questioning how to calculate the effective interest rate based on the repayments and the interest earned on those repayments. There is mention of a formula involving compounding interest, but clarity on its application is sought.

Discussion Status

The conversation is ongoing, with participants exploring different aspects of the problem. Some guidance has been offered regarding the repayment scheme and the calculation of returns, but no consensus or definitive method has been established yet.

Contextual Notes

There are references to the need for clarity on the nature of the payments (semiannual vs. annual) and the specifics of the repayment scheme, indicating potential confusion in the problem setup. The original poster's uncertainty about the correct forum for their question also highlights a lack of direction.

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
 
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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.
 
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 :smile:

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

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