Chapter 4: Effective and Nominal Interest Rates

Calculating Final Worth:

Investment = $500
Annual Interest earned = NOMINAL INTEREST RATE = 6% = 0.05
Quarterly Interest earned = (NOMINAL INTEREST RATE) / (4) = 6% / 4 = 1.5% = 0.015
So, (P = $500, i = 1.5%, and n = 12) and (F = P (F/P, i n) = 500(F/P, 1.5%, 12) = P(1 + 0.015) ^ 12) = $597.81
Now, if we didn’t convert the Nominal Interest Rate to a Quarterly Nominal Interest Rate, where (P = $500, i = 6%, and n = 3) and (F = P (F/P, i n) = 500(F/P, 6%, 3) = P(1 + 0.06) ^ 3) = $595.51

Calculating Effective Interest Rate

NOTICE: F=(500)(F/P, 1.5%, 12) = $597.81 is GREATER THAN F=(500)(F/P, 6%, 3)= $595.51
- This is why we need to calculate an EFFECTIVE ANNUAL INTEREST RATE
- Eff. Interest Rate = (1 + Quarterly Nominal Interest Rate) ^ (Quarters in a Year) = (1 + 0.015) ^ 4 = 6.136%

The Credit Card Offer Case: Tracy received a special offer of a new VISA credit card from Chase Bank linked with Southwest Airlines. It offers a generous bonus package for signing up by a specific date about 60 days from now. The bonus package includes extra airline points (once $3000 in purchases are made), priority airport check-in services (for 1 year), several free checked-bag allowances (for up to 10 check-ins), extra frequent-flyer points on the airline, access to airline lounges two times per year, plus several other rewards (rental car discounts, cruise trip amenities, and floral order discounts). The annual fee of $149 for membership does not start until the second year, and balance transfers from other credit cards have a low transfer fee, provided they are made at the time of initial membership.

If the new card is taken, Tracy will cancel the current card and transfer the $1000 balance to the new Chase Bank card. Tracy has a relatively low creditworthiness (low credit score) due to past missed and late monthly payments.

In the page that accompanies the offer letter, "pricing information" is included. This includes interest rates, interest charges, and fees. A summary of several of these rates and fees follows.

APR (annual percentage rate) for purchases and balance transfers*

18.99% per year (sum of the current U.S. Government prime rate of 3.25% and 15.74%, which is the APR added for a low credit score to determine the balance transfer APR for Chase Bank)

24.99% per year

29.99% per year (maximum penalty APR

APR for cash and overdraft advances*

Penalty APR for late minimum payment, exceeding credit limit, and returned unpaid payments"

Fees are listed as follows:

Annual membership

Balance transfer fees

Cash advances

$149; free the first year

$5 or 5% of each transfer, whichever is greater $10 or 5% of each advance, whichever is greater

Late payment

$39 each occurrence, if balance exceeds $250