Question 1194896: Please help with the homework:
Calculate the sum accrued on a fixed deposit of R10000 is invested on 15 march 2021 until 1 July 2023, if interest is credited annually on the 1 July at 15,5%.
Found 2 solutions by ElectricPavlov, ikleyn:
Answer by ElectricPavlov(122)   (Show Source):
You can put this solution on YOUR website! To calculate the accrued amount on a fixed deposit of R10,000 invested from 15 March 2021 to 1 July 2023, with interest credited annually on 1 July at an annual rate of 15.5%, follow these steps:
**1. Determine the Investment Period:**
- **Start Date:** 15 March 2021
- **End Date:** 1 July 2023
**2. Calculate the Total Investment Duration:**
- **From 15 March 2021 to 1 July 2023:**
- **Year 1:** 15 March 2021 to 1 July 2021
- **Days:** 15 March to 31 March (17 days) + April (30 days) + May (31 days) + June (30 days) + 1 July (1 day) = 109 days
- **Year 2:** 1 July 2021 to 1 July 2022
- **Days:** 365 days (non-leap year)
- **Year 3:** 1 July 2022 to 1 July 2023
- **Days:** 365 days
- **Total Days:** 109 + 365 + 365 = 839 days
- **Total Years:** 839 days ÷ 365 days/year ≈ 2.2986 years
**3. Apply the Compound Interest Formula:**
The compound interest formula is:
\[ A = P \times (1 + r)^t \]
Where:
- \( A \) = Accrued amount
- \( P \) = Principal amount (R10,000)
- \( r \) = Annual interest rate (15.5% or 0.155)
- \( t \) = Time in years (2.2986)
**4. Perform the Calculation:**
\[ A = 10,\!000 \times (1 + 0.155)^{2.2986} \]
First, calculate \( (1 + 0.155) \):
\[ 1 + 0.155 = 1.155 \]
Next, raise 1.155 to the power of 2.2986. Using a calculator:
\[ 1.155^{2.2986} \approx 1.404 \]
Now, multiply by the principal:
\[ A = 10,\!000 \times 1.404 = 14,\!040 \]
**5. Conclusion:**
The accrued amount on the fixed deposit of R10,000, invested from 15 March 2021 to 1 July 2023 at an annual interest rate of 15.5%, is approximately **R14,040**.
Answer by ikleyn(52858)  (Show Source):
You can put this solution on YOUR website! .
Calculations in the post by @ElectricPavlov are incorrect.
For example, he calculates 1.155^2.2986 and gets approximately 1.404,
which leads him to the answer 14,040.
Correct calculation is 1.155^2.2986 = 1.39267875, giving the final answer 13,926.79.
So, the answer R14,040 in the post by @ElectricPavlov is incorrect.
Also, from the problem, it is unclear, if the interest is simple or compounded,
so, the problem itself is dark and its meaning is unclear.
As the problem is worded and presented in the post, it is as far from to be
a true Math problem as the ground is far from the heaven.
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