Respuesta :
The amount that Wyatt’s effective interest rate is greater than his nominal interest rate is given by: Option D: 0.71% points
How to calculate compound interest's amount?
If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:
[tex]CI = P(1 +\dfrac{R}{100})^T - P[/tex]
The final amount becomes:
[tex]A = CI + P\\A = P(1 +\dfrac{R}{100})^T[/tex]
It is provided that:
Nominal interest rate = 13.62% compounding quarterly.
usually, interest rates are given in annual terms.
Converting 13.62 in quarterly terms, we get:
R = [tex]13.62/4 = 3.405\%[/tex] (as there are 4 quarters annually)
This rate is quarterly and is compounding quarterly.
Since these two things matched (the rate is in quarter version and so as the compounding of interest), we can take:
Unit of time = quarter of an year
Getting effective interest means interest that the principal grows by in one year.
One year = 4 quarters = 4 times unit of time.
Thus, T = 4
Thus, compound interest would be:
[tex]CI = P(1 +\dfrac{R}{100})^T - P = P( (1+3.405/100)^4 - 1) \approx P(0.1433)[/tex]
Taking its percent compared to principal amount P:
[tex]\dfrac{P(0.1433)}{P} \times 100 = 14.33\%[/tex]
Thus, the effective interest rate is 14.33%
The difference between effective and nominal interest rate is:
14.33 - 13.62 = 0.71%
Thus, the amount that Wyatt’s effective interest rate is greater than his nominal interest rate is given by: Option D: 0.71% points
Learn more about compound interest here:
https://brainly.com/question/11897800
