Question

2- A California bank, Berkeley Savings and Loan, advertised the following information: interest 7.55% and effective annual yield 7.842%. No mention is made of the interest period in the advertisement. Can you figure out the compounding scheme used by the bank?

Answer 1

Effective interest rate = (1+interest rate/m)^m - 1

0.07842 = (1+0.0755 / m)^m -1

(1+0.0755 / m)^m = 1.07842

using trail and error

When m = 2, (1+0.0755 / m)^m = 1.0769250

When m = 4,  (1+0.0755 / m)^m = 1.0776646

When m = 12,  (1+0.0755 / m)^m = 1.078168

When m = 365,  (1+0.0755 / m)^m = 1.0784148

When compounded continuously, e^0.0755 -1 = 1.0784232 - 1 = 0.07842 ~ 7.842

So compounding is done continuously