Rodriquez Davies
01/05/2023 · Elementary School
for mhen he son woe 7 years old. Adviser mode a depoit of 25 suo in the bank. The investmont gron at a simple interest rate and when Advisur's son was 28 years old, the value of the invest- ment was RII 972 , o0. At what rate the money nas invested
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Step-by-step Solution
Let's denote the principal amount (initial deposit) as \( P = 25 \) soles, the time period as \( t = 28 - 7 = 21 \) years, and the final amount as \( A = 972 \) soles.
The formula for calculating the final amount with simple interest is given by:
\[ A = P + P \times r \times t \]
where:
- \( A \) is the final amount,
- \( P \) is the principal amount,
- \( r \) is the interest rate,
- \( t \) is the time period in years.
We are given that \( A = 972 \), \( P = 25 \), and \( t = 21 \). We need to find the interest rate \( r \).
Substitute the given values into the formula:
\[ 972 = 25 + 25 \times r \times 21 \]
Now, we can solve for the interest rate \( r \) using the equation above.
Solve the equation by following steps:
- step0: Solve for \(r\):
\(972=25+25r\times 21\)
- step1: Multiply the terms:
\(972=25+525r\)
- step2: Swap the sides:
\(25+525r=972\)
- step3: Move the constant to the right side:
\(525r=972-25\)
- step4: Subtract the numbers:
\(525r=947\)
- step5: Divide both sides:
\(\frac{525r}{525}=\frac{947}{525}\)
- step6: Divide the numbers:
\(r=\frac{947}{525}\)
The interest rate at which the money was invested is approximately \( r = 1.803809523 \) or \( r = \frac{947}{525} \).
Quick Answer
The interest rate is approximately \( r = 1.803809523 \) or \( r = \frac{947}{525} \).
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