(State your reason why did you choose which one for the answer Thanks!!!!!) Give

Question

(State your reason why did you choose which one for the answer Thanks!!!!!)

Given an annual interest rate of 10%, when continuous compounding is used rather than monthly compounding, which of the following is correct?

A) Effective interest rate remains the same, but nominal interest rate increases.

B) Effective interest rate remains the same, but nominal interest rate decreases.

C) Nominal interest rate remains the same, but effective interest rate increases.

D) Nominal interest rate remains the same, but effective interest rate decreases.

Explanation / Answer

The correct answer is C) Nominal interest rate remains the same, but effective interest rate increases.

Reason: When compounding becomes continuous, the effective interest rate is expressed as follows:

Effective interest rate = er - 1, where e is the base of natural logarithm, and r is the nominal rate.

If the nominal interest rate is 12% for example, monthly compounding would increase the effective rate to 12.68%, whereas continuous compounding would increase the effective rate to 12.75%

Monthly compounding with 12% nominal rate of interest formula ( 1 + 0.12/12)12 -1

In continuous compounding the formula is e0.12 -1

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