To solve the equation [tex]\(15730400 = 14,000,000 \left(1 + \frac{R}{100}\right)^2\)[/tex] for [tex]\(R\)[/tex], follow these steps:
1. Identify the given constants and variables:
[tex]\[
A = 15,730,400 \quad \text{and} \quad P = 14,000,000
\][/tex]
Where [tex]\(A\)[/tex] is the future value and [tex]\(P\)[/tex] is the present value.
2. Rearrange the given equation:
[tex]\[
A = P \left(1 + \frac{R}{100}\right)^2
\][/tex]
Dividing both sides by [tex]\(P\)[/tex], we get:
[tex]\[
\frac{A}{P} = \left(1 + \frac{R}{100}\right)^2
\][/tex]
3. Calculate the ratio [tex]\( \frac{A}{P} \)[/tex]:
[tex]\[
\frac{15730400}{14000000} = 1.1236
\][/tex]
4. Take the square root of both sides to solve for [tex]\( \left(1 + \frac{R}{100}\right) \)[/tex]:
[tex]\[
\sqrt{1.1236} = 1 + \frac{R}{100}
\][/tex]
[tex]\[
1.06 = 1 + \frac{R}{100}
\][/tex]
5. Isolate [tex]\(R\)[/tex]:
Subtract 1 from both sides:
[tex]\[
1.06 - 1 = \frac{R}{100}
\][/tex]
[tex]\[
0.06 = \frac{R}{100}
\][/tex]
6. Multiply both sides by 100 to solve for [tex]\(R\)[/tex]:
[tex]\[
R = 0.06 \times 100
\][/tex]
[tex]\[
R = 6
\][/tex]
Therefore, the rate [tex]\(R\)[/tex] is 6%.
