Find the simple interest rate per cent per annum if $3,000 grows to $5,000 in 7 years.




To find the simple interest rate per annum, we can use the simple interest formula:

\[
A = P + SI
\]

Where:
- $ A $ is the final amount, $5,000.
- $ P $ is the principal amount, $3,000.
- $ SI $ is the simple interest, which is $ SI = P \times r \times t $.
- $ r $ is the rate of interest per annum.
- $ t $ is the time period in years, which is 7 years.

First, we need to find the simple interest ($ SI $):

\[
SI = A - P = 5000 - 3000 = 2000
\]

Now, we can use the formula to solve for $ r $:

\[
SI = P \times r \times t
\]

Substituting the values:

\[
2000 = 3000 \times r \times 7
\]

\[
2000 = 21000r
\]

\[
r = \frac{2000}{21000} = \frac{2}{21} \approx 0.0952
\]

To express $ r $ as a percentage:

\[
r \times 100 \approx 0.0952 \times 100 = 9.52\%
\]

So, the simple interest rate per annum is **9.52%**.

Would you like further details or have any questions?

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Here are some related questions for further exploration:

1. How would the interest rate change if the final amount was $6,000 instead?
2. What would be the interest rate if the period was reduced to 5 years?
3. How much interest would be earned if the rate was 10% instead of 9.52%?
4. What is the formula for compound interest, and how does it differ from simple interest?
5. How does time affect the amount of interest earned on a fixed principal?
6. What would be the future value if the rate was compounded annually?
7. How do you calculate the present value given the future value and interest rate?
8. What is the difference between nominal and effective interest rates?

**Tip:** Always remember to convert the interest rate into a percentage by multiplying by 100 when presenting the final answer.

Discover how to calculate the simple interest rate per annum when $3000 grows to $5000 over 7 years. Learn the step-by-step process with detailed formulas and calculations.

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