Certainly! Let's calculate the compound interest earned when [tex]$9800 is invested at 2% per annum for 4 years and 2 months.
1. Understand the Problem:
- Principal (P): $[/tex]9800
- Annual Interest Rate (r): 2% or 0.02
- Time (t): 4 years and 2 months
2. Convert Time to Years:
First, we need to convert the total time period from years and months to just years.
- There are 12 months in a year. So, 2 months is equivalent to [tex]\(\frac{2}{12} = 0.1667\)[/tex] years.
- Total time in years is then [tex]\( 4 + 0.1667 = 4.1667 \)[/tex] years.
3. Apply the Compound Interest Formula:
The compound interest formula is given by:
[tex]\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\][/tex]
In this case:
- [tex]\( P = 9800 \)[/tex]
- [tex]\( r = 0.02 \)[/tex]
- [tex]\( n = 1 \)[/tex] (since we are assuming the interest is compounded annually)
- [tex]\( t = 4.1667 \)[/tex]
4. Calculate the Amount (A):
Substituting the values, we get:
[tex]\[
A = 9800 \left(1 + 0.02\right)^{4.1667}
\][/tex]
After performing the calculations:
[tex]\[
A \approx 10642.90
\][/tex]
5. Compute the Compound Interest Earned:
The compound interest earned is the difference between the amount (A) and the principal (P).
[tex]\[
\text{Compound Interest} = A - P
\][/tex]
Substituting the values, we get:
[tex]\[
\text{Compound Interest} = 10642.90 - 9800 \approx 842.90
\][/tex]
Therefore, the compound interest earned when [tex]$9800 is invested at 2% per annum for 4 years and 2 months is approximately $[/tex]842.90. The total amount after this period would be about $10642.90.
