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:

  1. Nominal Annual Interest Rate (a): To be determined.
  2. Frequency of compounding (m): 12 (monthly compounding).
  3. 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:

Nominal Rate (a)=Interest Rate per Conversion Period×Frequency of Compounding (m)\text{Nominal Rate (a)} = \text{Interest Rate per Conversion Period} \times \text{Frequency of Compounding (m)}

Since the periodic interest rate is given as 0.07%0.07\%, we convert it to decimal form:

0.07%=0.07100=0.00070.07\% = \frac{0.07}{100} = 0.0007

Step 2: Calculate the Nominal Rate

Substituting the values:

a=0.0007×12a = 0.0007 \times 12

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:

  1. How does the nominal rate differ from the effective annual rate (EAR)?
  2. What happens to the nominal rate if the compounding frequency changes?
  3. How can we use this rate to calculate future value?
  4. What is the relationship between nominal and periodic interest rates?
  5. 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