Math Problem Statement
terest compounded =Monthly Nominal rate = a. Frequency of conversion m = 12 Interest rate per conversion period = 0.07%
Solution
To analyze this situation, let us calculate the following:
Known Variables:
- Nominal Annual Interest Rate (a): To be determined.
- Frequency of compounding (m): 12 (monthly compounding).
- Interest Rate per Conversion Period: 0.07% (per month).
Step 1: Nominal Rate Formula
The nominal annual interest rate is related to the periodic interest rate and compounding frequency as follows:
Since the periodic interest rate is given as , we convert it to decimal form:
Step 2: Calculate the Nominal Rate
Substituting the values:
a = 0.0084 \, \text{(or 0.84% per year nominally)}
Final Result:
The nominal annual interest rate (a) is 0.84% per year.
Let me know if you’d like a detailed explanation of compounding concepts, or have any specific questions!
Related Questions:
- How does the nominal rate differ from the effective annual rate (EAR)?
- What happens to the nominal rate if the compounding frequency changes?
- How can we use this rate to calculate future value?
- What is the relationship between nominal and periodic interest rates?
- Can the nominal rate be directly used to calculate interest accrued?
Tip:
Always convert percentages to decimals when performing calculations to avoid errors.
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Math Problem Analysis
Mathematical Concepts
Compound Interest
Nominal Interest Rate
Periodic Interest Rate
Formulas
Nominal Rate (a) = Interest Rate per Conversion Period × Frequency of Compounding (m)
Theorems
Compound Interest Formula
Suitable Grade Level
Grades 9-12
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