Question

INTEREST RATE The effective annual yield E for an account that is compounded n times per year at r percent is given by the formula E = [1 + (r/n)]^n - 1. Suppose an account pays 5%. Use a calculator to find how many compounding periods it would take for the effective yield to be 5.1%.

a) 6 compounding periods
b) 12 compounding periods
c) 24 compounding periods
d) 36 compounding periods

Answer 1

By using the formula for the effective annual yield, E = [1 + (r/n)]^n - 1, and substituting r = 5% and E = 5.1%, it was determined that 12 compounding periods would result in the desired effective yield. Therefore, the correct option is B.

Step-by-step explanation:

The effective annual yield (E) is calculated using the given formula: E = [1 + (r/n)]^n - 1. We need to find the number of compounding periods (n) that would result in an effective annual yield of 5.1% for an account paying 5% interest.

Let's substitute the given values into the formula to solve for n:

1. The nominal rate (r) is 5%, or 0.05 in decimal form.
2. We want the effective annual yield (E) to be 5.1%, or 0.051 in decimal form.
3. Now, we solve for n in the equation 0.051 = [1 + (0.05/n)]^n - 1.

To solve for n, we can either use trial and error with a calculator or use a more sophisticated mathematical tool like logarithms, iterative methods, or plug the equation into a software that can handle numerical analysis.

After testing each of the options provided (a) 6, (b) 12, (c) 24 and (d) 36 for n, we find that:

• n = 12 provides an effective yield closest to 5.1%.

Therefore, the answer is (b) 12 compounding periods.