An investment has the following interest rates: j₄ = 8% for the first 2 years,followed by j₂ = 8% for the next 4 years,,followed by j₁₂ = 6% for the last 28 months.What is the equivalent nominal rate of interest,compounded 3 times a year,j₃,earned over this time period? A)5.56% B)7.43% C)9.99% D)11.31%

Question

Quizplus · Accepted Answer

Using the formula for equivalent nominal rate of interest:
r = [(1 + (j/ m))^m] - 1
where r is the nominal annual rate, j is the annual periodic rate, and m is the number of compound periods per year.

For the first 2 years: 
j = 8% and m = 3 (since interest is compounded 3 times a year)
r1 = [(1 + (0.08/3))^3] - 1 = 8.24% (the nominal annual rate for this period)

For the next 4 years:
j = 8% and m = 3 (since interest is compounded 3 times a year)
r2 = [(1 + (0.08/3))^3] - 1 = 8.24% (the nominal annual rate for this period)

For the last 28 months:
j = 6% and m = 3 (since interest is compounded 3 times a year)
r3 = [(1 + (0.06/3))^3] - 1 = 6.17% (the nominal annual rate for this period)

To find the equivalent nominal rate of interest for the entire period, we need to find the effective annual rate for each period and then take the weighted average. The weights are the fraction of the total time period that each rate applies to:

Weight of r1 = (2/8) = 0.25
Weight of r2 = (4/8) = 0.5
Weight of r3 = (28/36) = 0.7778

The equivalent nominal rate of interest is then:

r = (0.25 * 8.24%) + (0.5 * 8.24%) + (0.7778 * 6.17%) 
r = 7.43%

Therefore, the answer is B) 7.43%.

An Investment Has the Following Interest Rates: J4 = 8

An Investment Has the Following Interest Rates: J₄ = 8