To find the principal amount (P) that amounts to $72,800 at simple interest in 4 years at an interest rate of 3% per annum, we can use the simple interest formula:
\[ A = P + I \]
Where:
- \( A \) = final amount ($72,800)
- \( P \) = principal amount
- \( I \) = interest earned
The interest (I) can be calculated using the formula:
\[ I = P \times r \times t \]
Where:
- \( r \) = interest rate (3% or 0.03)
- \( t \) = time (4 years)
Substituting this into our equation for \( A \):
\[ A = P + (P \times r \times t) \]
This can be simplified to:
\[ A = P(1 + r \times t) \]
Now we can substitute the values into the equation:
\[ 72800 = P(1 + 0.03 \times 4) \]
Calculating \( 0.03 \times 4 \):
\[ 0.03 \times 4 = 0.12 \]
Thus, the equation becomes:
\[ 72800 = P(1 + 0.12) \] \[ 72800 = P \times 1.12 \]
To find \( P \), we can rearrange the equation:
\[ P = \frac{72800}{1.12} \]
Calculating this gives:
\[ P = 65000 \]
Therefore, the principal amount is $65,000.
4 answers