Question

Find the principal which amounts to $72800 at simple interest in 4 years at 3% per annum

Answer 1

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**.