Question 1193578: Please help me with the homework.
1. 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 loan?
Answer by parmen(42)   (Show Source):
You can put this solution on YOUR website! ### 1.1. Amount the Client Will Receive
The client signs a note to pay \( M = 6000 \) in nine months. The bank uses a simple discount rate formula:
\[
PV = M \times (1 - d \times t)
\]
Where:
- \( M = 6000 \) (maturity value),
- \( d = 0.16 \) (simple discount rate per annum),
- \( t = \frac{9}{12} = 0.75 \) years (time until maturity).
Substituting:
\[
PV = 6000 \times (1 - 0.16 \times 0.75)
\]
\[
PV = 6000 \times (1 - 0.12)
\]
\[
PV = 6000 \times 0.88
\]
\[
PV = 5280
\]
The client will receive **R5280**.
---
### 1.2. Equivalent Simple Interest of the Loan
To find the equivalent simple interest, we first determine the **interest amount** and then calculate the equivalent simple interest rate (\( r \)).
#### Interest Amount:
\[
\text{Interest} = M - PV = 6000 - 5280 = 720
\]
#### Equivalent Simple Interest Formula:
\[
\text{Interest} = PV \times r \times t
\]
Rearranging for \( r \):
\[
r = \frac{\text{Interest}}{PV \times t}
\]
Substitute the values:
\[
r = \frac{720}{5280 \times 0.75}
\]
\[
r = \frac{720}{3960}
\]
\[
r \approx 0.1818 \, \text{or } 18.18\%
\]
The equivalent simple interest rate is **18.18% per annum**.
---
### Final Summary:
1. **Amount Received by the Client**: \( R5280 \)
2. **Equivalent Simple Interest Rate**: \( 18.18\% \) per annum
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