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A bank gives Rs. 25,000 on saving a certain principal in 2 years at 8% rate of interest. How much will the bank give (in Rs.) on the same principal in 4 years at the same rate of interest compounded annually?
- a)27,000
- b)29,000
- c)29,160
- d)27,080
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A bank gives Rs. 25,000 on saving a certain principal in 2 years at 8...
Understanding the Problem
To solve this problem, we need to find the principal amount based on the information given about the maturity amount after 2 years and then calculate the maturity amount after 4 years using compound interest.
Step 1: Finding the Principal Amount
- The bank gives Rs. 25,000 after 2 years at an 8% interest rate.
- Using the formula for compound interest:
A = P(1 + r/n)^(nt)
Here, A = Rs. 25,000, r = 8% or 0.08, n = 1 (compounded annually), t = 2 years.
- Rearranging the formula to find P:
P = A / (1 + r)^t
P = 25000 / (1 + 0.08)^2
P = 25000 / (1.08)^2
P = 25000 / 1.1664
P ≈ Rs. 21,429.24
Step 2: Calculating Amount after 4 Years
- Now, using the principal to calculate the amount after 4 years at the same interest rate:
A = P(1 + r)^t
A = 21429.24 * (1 + 0.08)^4
A = 21429.24 * (1.08)^4
A = 21429.24 * 1.36049
A ≈ Rs. 29,160.13
Conclusion
Thus, the bank will give approximately Rs. 29,160 after 4 years on the same principal amount at 8% interest compounded annually.
The correct answer is option 'C' - Rs. 29,160.
To solve this problem, we need to find the principal amount based on the information given about the maturity amount after 2 years and then calculate the maturity amount after 4 years using compound interest.
Step 1: Finding the Principal Amount
- The bank gives Rs. 25,000 after 2 years at an 8% interest rate.
- Using the formula for compound interest:
A = P(1 + r/n)^(nt)
Here, A = Rs. 25,000, r = 8% or 0.08, n = 1 (compounded annually), t = 2 years.
- Rearranging the formula to find P:
P = A / (1 + r)^t
P = 25000 / (1 + 0.08)^2
P = 25000 / (1.08)^2
P = 25000 / 1.1664
P ≈ Rs. 21,429.24
Step 2: Calculating Amount after 4 Years
- Now, using the principal to calculate the amount after 4 years at the same interest rate:
A = P(1 + r)^t
A = 21429.24 * (1 + 0.08)^4
A = 21429.24 * (1.08)^4
A = 21429.24 * 1.36049
A ≈ Rs. 29,160.13
Conclusion
Thus, the bank will give approximately Rs. 29,160 after 4 years on the same principal amount at 8% interest compounded annually.
The correct answer is option 'C' - Rs. 29,160.
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Community Answer
A bank gives Rs. 25,000 on saving a certain principal in 2 years at 8...
Given: A = Rs. 25,000, r = 8%, t = 2 years
We know that the formula for compound interest is:
... (i)According to the question, suppose Rs. x is the amount after 4 years. Then,
x = Rs. 29,160
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A bank gives Rs. 25,000 on saving a certain principal in 2 years at 8% rate of interest. How much will the bank give (in Rs.) on the same principal in 4 years at the same rate of interest compounded annually?a)27,000b)29,000c)29,160d)27,080Correct answer is option 'C'. Can you explain this answer?
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