The effective annual rate indicates which savings account will give the
highest returns on savings.
Reasons:
The nominal interest rate for Loan U, i = 9.97%
The compounding frequency of Loan U = Daily
The nominal interest rate for Loan V, i = 10.16%
The compounding frequency for Loan V = quarterly
Required:
The loan that as a lower effective interest rate.
Solution:
The effective (annual) interest rate, EAR, is given by the formula;
[tex]\displaystyle EAR = \mathbf{\left(1 + \frac{i}{n} \right)^n - 1}[/tex]
Where;
i = The given nominal interest rate
n = The number compounding periods (compounding frequency)
Therefore;
For Loan U, we have;
[tex]\displaystyle EAR_{Loan \, U} = \left(1 + \frac{0.0997}{365} \right)^{365} - 1 \approx 0.104824375 = \mathbf{ 10.482438\%}[/tex]
For Loan V, we have;
[tex]\displaystyle EAR_{Loan \, V} = \left(1 + \frac{0.1016}{4} \right)^4- 1 \approx 10.553692 \%[/tex]
The difference in the interest rate is 10.553692 - 10.482438 ≈ 0.07125
Learn more about the annual effective rate here:
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