Question 1196060: Please help me with the homework:
Calculate the sum accumulated on a fixed deposit of R10000 invested on the 15 march 2012 until 1 July 2014 and if interest is credited annually on the 01 July at the 15.5% per annum? Use fractional compound to calculate
Answer by ElectricPavlov(122)   (Show Source):
You can put this solution on YOUR website! To calculate the accumulated sum using **fractional compound interest**, we use the compound interest formula:
\[
A = P \cdot (1 + r)^t
\]
Where:
- \( A \) = Accumulated amount
- \( P \) = Principal = \( R10,000 \)
- \( r \) = Annual interest rate = \( 15.5\% = 0.155 \)
- \( t \) = Time in years
---
### **Step 1: Determine the Time Period (\( t \))**
1. Start date: **15 March 2012**
2. End date: **1 July 2014**
We calculate the total time in years:
- From **15 March 2012** to **15 March 2014** is exactly 2 years.
- From **15 March 2014** to **1 July 2014** is \( 3.5 \) months or \( \frac{3.5}{12} = 0.2917 \) years.
Total time:
\[
t = 2 + 0.2917 = 2.2917 \, \text{years}.
\]
---
### **Step 2: Apply the Compound Interest Formula**
Substitute the values into the formula:
\[
A = 10000 \cdot (1 + 0.155)^{2.2917}
\]
---
#### **Step 3: Break Down the Calculation**
1. Calculate \( (1 + 0.155) \):
\[
1 + 0.155 = 1.155
\]
2. Calculate \( (1.155)^{2.2917} \):
Using a calculator:
\[
(1.155)^{2.2917} \approx 1.3840
\]
3. Calculate the accumulated amount \( A \):
\[
A = 10000 \cdot 1.3840 = R13840.00
\]
---
### **Final Answer**
The accumulated sum on the fixed deposit is:
\[
\boxed{R13,840.00}
\]
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