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A certain sum of money amounts to rupees 2900 at 4% per annum in 4 years.In how many years will it amount to rupees 5000 at the same rate?
- a)20
- b)22
- c)24
- d)25
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A certain sum of money amounts to rupees 2900 at 4% per annum in 4 yea...
Answer – d) 25 Explanation : 2900 = p + p*(4/100)*4, p = 2500 5000 = 2500 + 2500*(4/100)*t
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A certain sum of money amounts to rupees 2900 at 4% per annum in 4 yea...
Given:
Principal amount = Rs. 2900
Rate of interest = 4% per annum
To find:
In how many years will the amount be Rs. 5000 at the same rate?
Solution:
Let's assume the number of years required is n.
Using the formula for compound interest, we can write:
Amount = Principal * (1 + Rate/100)^Time
For the first case, where the amount is Rs. 2900 after 4 years:
2900 = 2900 * (1 + 4/100)^4
1.04^4 = 2900 / 2900
1.04^4 = 1
Taking the fourth root on both sides:
1.04 = 1
So, for the given rate of interest, the amount remains the same after 4 years.
Now, let's find the number of years required for the amount to be Rs. 5000.
5000 = 2900 * (1 + 4/100)^n
Dividing both sides by 2900:
5000 / 2900 = (1 + 4/100)^n
1.72 = 1.04^n
Taking the logarithm of both sides:
log(1.72) = log(1.04^n)
Using the property log(a^b) = b * log(a):
log(1.72) = n * log(1.04)
Dividing both sides by log(1.04):
n = log(1.72) / log(1.04)
Using a calculator, we can find the value of n to be approximately 25.12.
Therefore, the amount will be Rs. 5000 in approximately 25 years.
Hence, the correct option is (D) 25.
Principal amount = Rs. 2900
Rate of interest = 4% per annum
To find:
In how many years will the amount be Rs. 5000 at the same rate?
Solution:
Let's assume the number of years required is n.
Using the formula for compound interest, we can write:
Amount = Principal * (1 + Rate/100)^Time
For the first case, where the amount is Rs. 2900 after 4 years:
2900 = 2900 * (1 + 4/100)^4
1.04^4 = 2900 / 2900
1.04^4 = 1
Taking the fourth root on both sides:
1.04 = 1
So, for the given rate of interest, the amount remains the same after 4 years.
Now, let's find the number of years required for the amount to be Rs. 5000.
5000 = 2900 * (1 + 4/100)^n
Dividing both sides by 2900:
5000 / 2900 = (1 + 4/100)^n
1.72 = 1.04^n
Taking the logarithm of both sides:
log(1.72) = log(1.04^n)
Using the property log(a^b) = b * log(a):
log(1.72) = n * log(1.04)
Dividing both sides by log(1.04):
n = log(1.72) / log(1.04)
Using a calculator, we can find the value of n to be approximately 25.12.
Therefore, the amount will be Rs. 5000 in approximately 25 years.
Hence, the correct option is (D) 25.
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A certain sum of money amounts to rupees 2900 at 4% per annum in 4 years.In how many years will it amount to rupees 5000 at the same rate?a)20b)22c)24d)25e)None of theseCorrect answer is option 'D'. Can you explain this answer?
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