The interest rate on a personal loan is 4% per month. What is the effective rate? Group of answer choices 60.10% p.a. compounded monthly 160.1% p.a. compounded annually 60.1% p.a. compounded yearly 48% p.a. compounded monthly
Question
The interest rate on a personal loan is 4% per month. What is the effective rate?
Group of answer choices
60.10% p.a. compounded monthly
160.1% p.a. compounded annually
60.1% p.a. compounded yearly
48% p.a. compounded monthly
Solution
The effective annual rate (EAR) can be calculated using the formula:
EAR = (1 + r)^n - 1
where:
- r is the nominal interest rate per period (4% or 0.04 per month)
- n is the number of periods in a year (12 months)
Substituting the given values into the formula, we get:
EAR = (1 + 0.04)^12 - 1
Calculating this expression, we find that the effective annual rate is approximately 60.10% p.a. Therefore, the correct answer is 60.10% p.a. compounded monthly.
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