Certainly! To determine the value of a packet of rice costing K5.00 in five years, given an annual increase rate of 8%, we can use the compound interest formula which is generally used for such calculations.
The compound interest formula is:
[tex]\[ \text{Future Value} = \text{Present Value} \times (1 + r)^n \][/tex]
Where:
- [tex]\(\text{Future Value}\)[/tex] is the value after n years.
- [tex]\(\text{Present Value}\)[/tex] is the initial value (in this case, K5.00).
- [tex]\(r\)[/tex] is the annual rate of increase (in this case, 8% or 0.08).
- [tex]\(n\)[/tex] is the number of years (in this case, 5).
Let's break it down year by year to see how the value changes:
1. Initial Value:
[tex]\[ \text{Present Value} = K5.00 \][/tex]
2. After 1 year:
[tex]\[ \text{Value After 1 Year} = 5.00 \times (1 + 0.08) = 5.00 \times 1.08 \][/tex]
3. After 2 years:
[tex]\[ \text{Value After 2 Years} = (5.00 \times 1.08) \times 1.08 = 5.00 \times 1.08^2 \][/tex]
4. After 3 years:
[tex]\[ \text{Value After 3 Years} = (5.00 \times 1.08^2) \times 1.08 = 5.00 \times 1.08^3 \][/tex]
5. After 4 years:
[tex]\[ \text{Value After 4 Years} = (5.00 \times 1.08^3) \times 1.08 = 5.00 \times 1.08^4 \][/tex]
6. After 5 years:
[tex]\[ \text{Value After 5 Years} = (5.00 \times 1.08^4) \times 1.08 = 5.00 \times 1.08^5 \][/tex]
Thus, the value of the packet of rice after 5 years is:
[tex]\[ 5.00 \times (1.08)^5 \][/tex]
Based on this calculation, we find:
[tex]\[ 5.00 \times 1.08^5 = 7.35 \][/tex]
So, the value of the packet of rice in five years will be approximately K7.35.
Therefore, the correct answer is:
B. K7.35
