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A sum of Rs. 400 amounts to Rs. 480 in 4 years. What will it amount to if the rate of interest is increased by 2 % for the same time?
- a)Rs. 512
- b)520Rs.
- c)Rs.490
- d)Rs.515
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A sum of Rs. 400 amounts to Rs. 480 in 4 years. What will it amount t...
We know that, S.I = P x R x T / 100
A = S.I + P
480 = 5.1+400
⇒S.I = 480 − 400 = 80
⇒S.I = P × R × T100
⇒80 = 400 × R × 4100
⇒R = 5%
Now rate is increased by 2% So, new rate is 7% New S.I=400 × 7 × 4 / 100 = Rs.112
New Amount = S.I + P = 112 + 400 = Rs.512
Most Upvoted Answer
A sum of Rs. 400 amounts to Rs. 480 in 4 years. What will it amount t...
Given:
Principal amount (P) = Rs. 400
Amount after 4 years (A) = Rs. 480
To find:
Amount after 4 years with an increased interest rate of 2%
Solution:
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
Where:
A = Amount after time t
P = Principal amount
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Time in years
In this case, the interest is compounded annually, so n = 1.
Step 1: Calculate the interest rate
We can find the interest rate using the formula:
r = (A/P)^(1/nt) - 1
Substituting the given values, we get:
r = (480/400)^(1/(1*4)) - 1
r = (1.2)^(1/4) - 1
Step 2: Calculate the new interest rate
We need to increase the interest rate by 2%. Let's assume the new interest rate is r'.
r' = r + (2/100) * r
r' = r(1 + 0.02)
r' = r * 1.02
Step 3: Calculate the new amount
Using the formula for compound interest, we can find the new amount (A'):
A' = P(1 + r'/n)^(nt)
A' = 400(1 + r'/1)^(1*4)
Substituting the value of r', we get:
A' = 400(1 + r * 1.02)^(4)
A' = 400(1.02r)^4
Step 4: Calculate the final amount
Now, substitute the value of r from step 1 into the formula for A':
A' = 400(1.02^(1/4))^4
A' = 400(1.02)^4
Calculating this value, we find:
A' ≈ 511.22
Therefore, the amount after 4 years with an increased interest rate of 2% is approximately Rs. 511.22, which can be rounded to Rs. 512 (option A).
Principal amount (P) = Rs. 400
Amount after 4 years (A) = Rs. 480
To find:
Amount after 4 years with an increased interest rate of 2%
Solution:
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
Where:
A = Amount after time t
P = Principal amount
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Time in years
In this case, the interest is compounded annually, so n = 1.
Step 1: Calculate the interest rate
We can find the interest rate using the formula:
r = (A/P)^(1/nt) - 1
Substituting the given values, we get:
r = (480/400)^(1/(1*4)) - 1
r = (1.2)^(1/4) - 1
Step 2: Calculate the new interest rate
We need to increase the interest rate by 2%. Let's assume the new interest rate is r'.
r' = r + (2/100) * r
r' = r(1 + 0.02)
r' = r * 1.02
Step 3: Calculate the new amount
Using the formula for compound interest, we can find the new amount (A'):
A' = P(1 + r'/n)^(nt)
A' = 400(1 + r'/1)^(1*4)
Substituting the value of r', we get:
A' = 400(1 + r * 1.02)^(4)
A' = 400(1.02r)^4
Step 4: Calculate the final amount
Now, substitute the value of r from step 1 into the formula for A':
A' = 400(1.02^(1/4))^4
A' = 400(1.02)^4
Calculating this value, we find:
A' ≈ 511.22
Therefore, the amount after 4 years with an increased interest rate of 2% is approximately Rs. 511.22, which can be rounded to Rs. 512 (option A).
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A sum of Rs. 400 amounts to Rs. 480 in 4 years. What will it amount to if the rate of interest is increased by 2 % for the same time?a)Rs. 512b)520Rs.c)Rs.490d)Rs.515Correct answer is option 'A'. Can you explain this answer?
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