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There is 100% increase to an amount in 8 years, at simple interest. Find the compound interest of Rs. 8000 after 2 years at the same rate of interest.
- a)Rs. 2500
- b)Rs. 2000
- c)Rs. 2250
- d)Rs. 2125
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
There is 100% increase to an amount in 8 years, at simple interest. Fi...
Formulas to be used: -
SI = ( P × r × t ) / 100
For CI:
Where SI is Simple interest,
A is the amount at the end of time t,
P is the principal,
t is time,
r is rate
For SI, there is 100% increase to amount, thus A = 2P
⇒ SI = p
Time is 8 years.
∴ p = (p × r × t)/100
⇒ r = 100/8 = 12.5%
Now, P = 8000, t = 2years and r = 12.5%
⇒ A = 8000 × 1.1252
⇒ A = Rs. 10125
CI = A – P
⇒ CI = 10125 – 8000 = Rs. 2125
SI = ( P × r × t ) / 100
For CI:
Where SI is Simple interest,
A is the amount at the end of time t,
P is the principal,
t is time,
r is rate
For SI, there is 100% increase to amount, thus A = 2P
⇒ SI = p
Time is 8 years.
∴ p = (p × r × t)/100
⇒ r = 100/8 = 12.5%
Now, P = 8000, t = 2years and r = 12.5%
⇒ A = 8000 × 1.1252
⇒ A = Rs. 10125
CI = A – P
⇒ CI = 10125 – 8000 = Rs. 2125
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There is 100% increase to an amount in 8 years, at simple interest. Fi...
Given:
- Amount = Rs. 8000
- Time = 2 years
- Rate of interest = same as the rate of interest for simple interest, which resulted in a 100% increase in 8 years
To Find:
Compound interest after 2 years
Solution:
To find the compound interest, we need to calculate the compound amount at the end of 2 years and then subtract the principal amount to get the compound interest.
Step 1: Calculate the compound amount
The formula to calculate compound amount is:
A = P(1 + r/n)^(nt)
Where,
A = Compound Amount
P = Principal Amount
r = Rate of Interest
n = Number of times interest is compounded per year
t = Time in years
In this case, the interest is compounded annually, so n = 1.
Given:
P = Rs. 8000
t = 2 years
The formula becomes:
A = 8000(1 + r/1)^(1*2)
A = 8000(1 + r)^2
Step 2: Calculate the rate of interest
We are given that there is a 100% increase in 8 years at simple interest. This means that the amount becomes double in 8 years.
Let's assume the rate of interest is x.
So, after 8 years, the compound amount would be:
A = 8000(1 + x)^8
According to the given information, the amount becomes double in 8 years:
2 * 8000 = 8000(1 + x)^8
16000 = 8000(1 + x)^8
Simplifying the equation:
2 = (1 + x)^8
Taking the 8th root on both sides:
1 + x = √2
x = √2 - 1
Step 3: Calculate the compound amount after 2 years
Now, substitute the value of x in the compound amount formula:
A = 8000(1 + (√2 - 1))^2
Solving the equation:
A = 8000(1 + 1.414 - 1)^2
A = 8000(1.414)^2
A = 8000(1.998996)
A ≈ 15991.97
Step 4: Calculate the compound interest
Compound Interest = Compound Amount - Principal Amount
Compound Interest = 15991.97 - 8000
Compound Interest ≈ 7991.97
Therefore, the compound interest of Rs. 8000 after 2 years at the same rate of interest is approximately Rs. 7991.97, which is closest to option 'D' (Rs. 2125).
- Amount = Rs. 8000
- Time = 2 years
- Rate of interest = same as the rate of interest for simple interest, which resulted in a 100% increase in 8 years
To Find:
Compound interest after 2 years
Solution:
To find the compound interest, we need to calculate the compound amount at the end of 2 years and then subtract the principal amount to get the compound interest.
Step 1: Calculate the compound amount
The formula to calculate compound amount is:
A = P(1 + r/n)^(nt)
Where,
A = Compound Amount
P = Principal Amount
r = Rate of Interest
n = Number of times interest is compounded per year
t = Time in years
In this case, the interest is compounded annually, so n = 1.
Given:
P = Rs. 8000
t = 2 years
The formula becomes:
A = 8000(1 + r/1)^(1*2)
A = 8000(1 + r)^2
Step 2: Calculate the rate of interest
We are given that there is a 100% increase in 8 years at simple interest. This means that the amount becomes double in 8 years.
Let's assume the rate of interest is x.
So, after 8 years, the compound amount would be:
A = 8000(1 + x)^8
According to the given information, the amount becomes double in 8 years:
2 * 8000 = 8000(1 + x)^8
16000 = 8000(1 + x)^8
Simplifying the equation:
2 = (1 + x)^8
Taking the 8th root on both sides:
1 + x = √2
x = √2 - 1
Step 3: Calculate the compound amount after 2 years
Now, substitute the value of x in the compound amount formula:
A = 8000(1 + (√2 - 1))^2
Solving the equation:
A = 8000(1 + 1.414 - 1)^2
A = 8000(1.414)^2
A = 8000(1.998996)
A ≈ 15991.97
Step 4: Calculate the compound interest
Compound Interest = Compound Amount - Principal Amount
Compound Interest = 15991.97 - 8000
Compound Interest ≈ 7991.97
Therefore, the compound interest of Rs. 8000 after 2 years at the same rate of interest is approximately Rs. 7991.97, which is closest to option 'D' (Rs. 2125).
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There is 100% increase to an amount in 8 years, at simple interest. Find the compound interest of Rs. 8000 after 2 years at the same rate of interest.a)Rs. 2500b)Rs. 2000c)Rs. 2250d)Rs. 2125Correct answer is option 'D'. Can you explain this answer?
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