SOLUTION: Please help me with the homework The simple discount rate of a bank is 16% per annum. If a client signs a note to pay 6000 in nine months time: 1.1. how much will the client rece

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Question 1193569: Please help me with the homework
The simple discount rate of a bank is 16% per annum. If a client signs a note to pay 6000 in nine months time:
1.1. how much will the client receive?
1.2. what is the equivalent simple interest of the this loan?
Found 2 solutions by parmen, ikleyn:
Answer by parmen(42) About Me  (Show Source):
You can put this solution on YOUR website!
**1.1. Calculate the amount the client receives:**
* **Calculate the discount:**
* Discount = Face Value * Discount Rate * Time
= $6000 * 0.16 * (9/12)
= $72
* **Amount received by the client:**
* Amount Received = Face Value - Discount
= $6000 - $72
= $5928
**1.2. Calculate the equivalent simple interest rate**
* **Find the effective discount rate:**
* Effective Discount Rate = (Discount / Face Value) * (12 / Time in months)
= ($72 / $6000) * (12 / 9)
= 0.016 * 4/3
= 0.02133
* **Calculate the equivalent simple interest rate:**
* Equivalent Simple Interest Rate = (Discount / Present Value) * (12 / Time in months)
= ($72 / $5928) * (12 / 9)
= 0.01618
* **Express as a percentage:**
* Equivalent Simple Interest Rate = 0.01618 * 100 = 1.618%
**Therefore:**
* **1.1. The client will receive $5928.**
* **1.2. The equivalent simple interest rate of the loan is approximately 1.62% per annum.**

Answer by ikleyn(52769) About Me  (Show Source):
You can put this solution on YOUR website!
.
Please help me with the homework
The simple discount rate of a bank is 16% per annum. If a client signs a note to pay 6000 in nine months time:
1.1. how much will the client receive?
1.2. what is the equivalent simple interest of the this loan?
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        Calculations in the post by @parmen are incorrect.
        I came to bring a correct solution. 


**1.1. Calculate the amount the client receives:**

* **Calculate the discount:**
    * Discount = Face Value * Discount Rate * Time 
                = $6000 * 0.16 * (9/12) 
                = $720

* **Amount received by the client:**
    * Amount Received = Face Value - Discount
                        = $6000 - $720
                        = $5280

**1.2. Calculate the equivalent simple interest rate**

* **Find the effective discount rate:**
    * Effective Discount Rate = (Discount / Face Value) * (12 / Time in months) 
                               = ($720 / $6000) * (12 / 9) 
                               = 0.16 * 4/3 
                               = 0.2133 

* **Calculate the equivalent simple interest rate:**
    * Equivalent Simple Interest Rate = (Discount / Present Value) * (12 / Time in months)
                                  = ($720 / $5280) * (12 / 9) 
                                  = 0.1818 

* **Express as a percentage:**
    * Equivalent Simple Interest Rate = 0.1618 * 100 = 18.18%

**Therefore:**

* **1.1. The client will receive $5280.**
* **1.2. The equivalent simple interest rate of the loan is approximately 18.2% per annum.**

Solved (correctly).