To find the total amount and the interest earned on [tex]$5,000 at 8\% annual interest for 20 years with interest compounded annually, we can use the provided compound interest table.
The steps for solving this are:
1. Identify the Given Data:
- Principal (P): $[/tex]5000
- Annual Interest Rate (R): 8%
- Period (T): 20 years
2. Locate the Compound Factor:
- Since the interest is compounded annually, for 20 years at an 8% annual interest rate, we directly look at the compound factor from the table at the intersection of 20 periods and 8% interest rate.
- From the table, we find this value to be 4.6609571.
3. Calculate the Total Amount (A):
- The formula for the total amount with compound interest is:
[tex]\[
A = P \times (1 + \frac{R}{100})^T
\][/tex]
- Using the compound factor from the table directly:
[tex]\[
A = Principal \times \text{Compound Factor}
\][/tex]
[tex]\[
A = 5000 \times 4.6609571
\][/tex]
[tex]\[
A = 23304.7855
\][/tex]
4. Calculate the Interest Earned (I):
- The interest earned is the total amount minus the principal:
[tex]\[
I = A - P
\][/tex]
[tex]\[
I = 23304.7855 - 5000
\][/tex]
[tex]\[
I = 18304.7855
\][/tex]
Therefore, the total amount after 20 years is [tex]$23,304.7855, and the interest earned is $[/tex]18,304.7855.
