Calulate the effective interest rate. ### Educational Exercise: Calculating the Effective Interest Rate#### Problem StatementYou have the option to choose between a simple interest note or a simple discount note under the following terms:- Principal Amount: $29,059- Interest Rate: 8% - Duration: 12 months#### Tasksa. **Calculate the Effective Interest Rate** - Do not round intermediate calculations. - Round your final answer to the nearest tenth percent. **Input Box:** - Effective interest rate: _______ %b. **Decision Based on Effective Interest Rate** - Which option would you choose? - [ ] Simple discount note#### Instructions1. Use the appropriate formulas for calculating the effective interest rate for both the simple interest note and the simple discount note.2. Compare the effective interest rates obtained from each method.3. Determine which option provides a more favorable rate based on your calculations. This exercise helps in understanding the differences between simple interest and simple discount notes, as well as the impact of these types on the effective interest rate calculations.

Answered: Calulate the effective interest rate.

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

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Calulate the effective interest rate.

### Educational Exercise: Calculating the Effective Interest Rate

#### Problem Statement

You have the option to choose between a simple interest note or a simple discount note under the following terms:

- Principal Amount: $29,059
- Interest Rate: 8%
- Duration: 12 months

#### Tasks

a. **Calculate the Effective Interest Rate**

- Do not round intermediate calculations.
- Round your final answer to the nearest tenth percent.

**Input Box:**
- Effective interest rate: _______ %

b. **Decision Based on Effective Interest Rate**

- Which option would you choose?
- [ ] Simple discount note

#### Instructions

1. Use the appropriate formulas for calculating the effective interest rate for both the simple interest note and the simple discount note.
2. Compare the effective interest rates obtained from each method.
3. Determine which option provides a more favorable rate based on your calculations.

This exercise helps in understanding the differences between simple interest and simple discount notes, as well as the impact of these types on the effective interest rate calculations.

Expert Solution

Step 1

Here,

Value of Note is $29,059

Simple Interest Rate is 8%

Time Duration of Note is 12 months

Step 2 a) Calculation of Effective Interest Rate:

The effective interest rate of a simple interest note will remain 8 % only as the value of the note will remain the same.

In order to calculate the effective Interest rate, we need to calculate the value of simple discount note which is as follows:

Calculation of Interest on Note is as follows:

$\begin{array}{rcl} S i m p l e I n t e r e s t & = & P R T \\ = & $ 29, 059 \times . 08 \times \frac{12}{12} \\ = & $ 2, 324.72 \end{array}$

Calculation of Value of Simple Discount Note is as follows:

$\begin{array}{rcl} V a l u e o f S i m p l e D i s c o u n t N o t e & = & P r i n c i p a l - I n t e r e s t \\ = & $ 29, 059 - $ 2, 324.72 \\ = & $ 26, 734.28 \end{array}$

Calculation of Effective Interest Rate is as follows:

$\begin{array}{rcl} E f f e c t i v e I n t e r e s t R a t e & = & \frac{I n t e r e s t A m o u n t}{V a l u e o f D i s c o u n t N o t e} \\ = & \frac{$ 2, 324.72}{$ 26, 734.28} \\ = & 0.08695652173 \\ = & 8.70 % \end{array}$

Answer: Effective Interest Rate is 8.70%

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