Calculating Annual Effective Rate of Interest: A Comprehensive Guide

In summary, the question is asking how to find the annual effective rate of interest for a loan of $15 000 with a 9% annual interest rate, to be repaid in 16 semi-annual installments over an 8-year period. The borrower then invests each repayment, earning 7% annual interest. The annual effective rate of interest earned over the entire 8-year period is 8.17%.
  • #1
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
 
Physics news on Phys.org
  • #2
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.
 
  • #4
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.
 

1. What is the Annual Effective Rate of Interest (AER)?

The Annual Effective Rate of Interest (AER) is the actual annual rate of interest that is earned on an investment or loan. It takes into account the compounding of interest over the course of a year, making it a more accurate measure of the true cost or return on an investment.

2. How is the AER calculated?

The AER is calculated by multiplying the stated interest rate by the number of compounding periods in a year. This result is then raised to the power of the number of years, and any additional fees or charges are added to the total. The final step is to subtract the initial principal amount from the total to get the annual effective rate of interest.

3. How is the AER different from the Annual Percentage Rate (APR)?

The AER takes into account the compounding of interest, while the APR does not. This means that the AER will always be higher than the APR, as it reflects the true cost or return on an investment over a year. The APR, on the other hand, only considers the stated interest rate.

4. Why is it important to calculate the AER?

Calculating the AER is important because it gives a more accurate representation of the true cost or return on an investment. This allows individuals to compare different investments or loans more effectively and make informed decisions about their finances.

5. How can I use the AER to compare different investments or loans?

The AER can be used to compare different investments or loans by providing a standard measure of the annual interest rate for each option. This allows individuals to see which option will give them the highest return or cost them the least in interest, making it easier to choose the best option for their financial goals.

Similar threads

Simple Interest for two investments
    • Precalculus Mathematics Homework Help
Replies
9
Views
2K
Student Loan Payment Calculation and Effective Interest Rate Analysis
    • Precalculus Mathematics Homework Help
Replies
14
Views
7K
MHB Mortgage Calc: Calculate Payment, Owed & Interest Breakdown
    • General Math
Replies
1
Views
2K
MHB Effective Rate of Interest
    • General Math
Replies
2
Views
1K
Finance math: find total interest rate
    • Precalculus Mathematics Homework Help
Replies
1
Views
2K
Calculating Annual Effective Interest Rate for Financial Mathematics
    • Calculus and Beyond Homework Help
Replies
2
Views
2K
MHB Find Constant % of Annual Salary to Reach Retirement Goal
    • General Math
Replies
9
Views
2K
MHB Solve Annuities Questions: BA II Plus Calculator
    • General Math
Replies
2
Views
1K
Finding the Optimal Rate for Equal Interest Earnings on Savings Accounts
    • Precalculus Mathematics Homework Help
Replies
2
Views
3K
Calculating Present Value of a Growing Annuity with Monthly Payments
    • Calculus and Beyond Homework Help
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top