Math / Numbers & Operations

QuestionA certain sum of money will amount to $₹ 19600$ at the rate of $8 \%$ per annum simple interest at the end of 5 years. Find the money.

Studdy Solution

STEP 1

1. We are given the final amount after 5 years, which is ₹ 19600.
2. The rate of simple interest is 8% per annum.
3. The time period is 5 years.
4. We need to find the principal amount (initial sum of money).

STEP 2

1. Understand the formula for simple interest.
2. Set up the equation using the given values.
3. Solve for the principal amount.

STEP 3

The formula for simple interest is given by $SI = \frac{P \cdot R \cdot T}{100}$ , where: - $SI$ is the simple interest, - $P$ is the principal, - $R$ is the rate of interest per annum, - $T$ is the time in years.

STEP 4

The total amount $A$ after time $T$ is given by: $A = P + SI$ Given $A = 19600$ , $R = 8\%$ , and $T = 5$ years, we need to find $P$ .

STEP 5

Substitute the simple interest formula $SI = \frac{P \cdot R \cdot T}{100}$ into the total amount formula: $19600 = P + \frac{P \cdot 8 \cdot 5}{100}$

STEP 6

Simplify the equation: $19600 = P + \frac{40P}{100}$

STEP 7

Convert the fraction to a decimal: $19600 = P + 0.4P$

STEP 8

Combine like terms: $19600 = 1.4P$

STEP 9

Solve for $P$ by dividing both sides by 1.4: $P = \frac{19600}{1.4}$

STEP 10

Calculate the value: $P = 14000$
Solution: The principal amount is ₹ 14000.

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QuestionA certain sum of money will amount to $₹ 19600$ at the rate of $8 \%$ per annum simple interest at the end of 5 years. Find the money.

Studdy Solution

STEP 1

1. We are given the final amount after 5 years, which is ₹ 19600.
2. The rate of simple interest is 8% per annum.
3. The time period is 5 years.
4. We need to find the principal amount (initial sum of money).

STEP 2

1. Understand the formula for simple interest.
2. Set up the equation using the given values.
3. Solve for the principal amount.

STEP 3

The formula for simple interest is given by $SI = \frac{P \cdot R \cdot T}{100}$ , where: - $SI$ is the simple interest, - $P$ is the principal, - $R$ is the rate of interest per annum, - $T$ is the time in years.

STEP 4

The total amount $A$ after time $T$ is given by: $A = P + SI$ Given $A = 19600$ , $R = 8\%$ , and $T = 5$ years, we need to find $P$ .

STEP 5

Substitute the simple interest formula $SI = \frac{P \cdot R \cdot T}{100}$ into the total amount formula: $19600 = P + \frac{P \cdot 8 \cdot 5}{100}$

STEP 6

Simplify the equation: $19600 = P + \frac{40P}{100}$

STEP 7

Convert the fraction to a decimal: $19600 = P + 0.4P$

STEP 8

Combine like terms: $19600 = 1.4P$

STEP 9

Solve for $P$ by dividing both sides by 1.4: $P = \frac{19600}{1.4}$

STEP 10

Calculate the value: $P = 14000$
Solution: The principal amount is ₹ 14000.

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QuestionA certain sum of money will amount to ₹19600₹ 19600₹19600 at the rate of 8%8 \%8% per annum simple interest at the end of 5 years. Find the money.

Studdy Solution

STEP 1

1. We are given the final amount after 5 years, which is ₹ 19600.2. The rate of simple interest is 8% per annum.3. The time period is 5 years.4. We need to find the principal amount (initial sum of money).

STEP 2

1. Understand the formula for simple interest.2. Set up the equation using the given values.3. Solve for the principal amount.

STEP 3

The formula for simple interest is given by SI=P⋅R⋅T100 SI = \frac{P \cdot R \cdot T}{100} SI=100P⋅R⋅T​, where: - SI SI SI is the simple interest, - P P P is the principal, - R R R is the rate of interest per annum, - T T T is the time in years.

STEP 4

The total amount A A A after time T T T is given by: A=P+SI A = P + SI A=P+SI Given A=19600 A = 19600 A=19600, R=8% R = 8\% R=8%, and T=5 T = 5 T=5 years, we need to find P P P.

STEP 5

Substitute the simple interest formula SI=P⋅R⋅T100 SI = \frac{P \cdot R \cdot T}{100} SI=100P⋅R⋅T​ into the total amount formula: 19600=P+P⋅8⋅5100 19600 = P + \frac{P \cdot 8 \cdot 5}{100} 19600=P+100P⋅8⋅5​

STEP 6

Simplify the equation: 19600=P+40P100 19600 = P + \frac{40P}{100} 19600=P+10040P​

STEP 7

Convert the fraction to a decimal: 19600=P+0.4P 19600 = P + 0.4P 19600=P+0.4P

STEP 8

Combine like terms: 19600=1.4P 19600 = 1.4P 19600=1.4P

STEP 9

Solve for P P P by dividing both sides by 1.4: P=196001.4 P = \frac{19600}{1.4} P=1.419600​

STEP 10

Calculate the value: P=14000 P = 14000 P=14000 Solution: The principal amount is ₹ 14000.

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Studdy solves anything!

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QuestionA certain sum of money will amount to $₹ 19600$ at the rate of $8 \%$ per annum simple interest at the end of 5 years. Find the money.

1. We are given the final amount after 5 years, which is ₹ 19600.
2. The rate of simple interest is 8% per annum.
3. The time period is 5 years.
4. We need to find the principal amount (initial sum of money).

1. Understand the formula for simple interest.
2. Set up the equation using the given values.
3. Solve for the principal amount.

The formula for simple interest is given by $SI = \frac{P \cdot R \cdot T}{100}$ , where: - $SI$ is the simple interest, - $P$ is the principal, - $R$ is the rate of interest per annum, - $T$ is the time in years.

The total amount $A$ after time $T$ is given by: $A = P + SI$ Given $A = 19600$ , $R = 8\%$ , and $T = 5$ years, we need to find $P$ .

Substitute the simple interest formula $SI = \frac{P \cdot R \cdot T}{100}$ into the total amount formula: $19600 = P + \frac{P \cdot 8 \cdot 5}{100}$

Simplify the equation: $19600 = P + \frac{40P}{100}$

Convert the fraction to a decimal: $19600 = P + 0.4P$

Combine like terms: $19600 = 1.4P$

Solve for $P$ by dividing both sides by 1.4: $P = \frac{19600}{1.4}$

Calculate the value: $P = 14000$
Solution: The principal amount is ₹ 14000.