How much will Rs 25000 amount to in 2 years at compound interest, if the rates for 1st and 2nd years be 4% and 5% p.a. respectively?
Solution
Here P = Rs.25000, t = 2 years, r = 4%, 5% successively.
Now, Amount
= `"P"(1 + "r"_1/100)(1 + "r"_2/100)`
= `25000(1 + 4/100)(1 + 5/100)`
= `25000(104/100)(105/100)`
= 27300
Hence, Amount = Rs.27300.
Concept: Concept of Compound Interest - Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years
Is there an error in this question or solution?
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Correct Option: C
Let the rate percent per annum be r.
Given that , P = ₹ 2304 , A = ₹ 2500 , n = 2 years
Using the given formula ,
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A = P | 1 + | r | n | ||
100 |
2500 = 2304 | 1 + | r | 2 | ||
100 |
⇒ | 1 + | r | 2 | = | 2500 | = | 50 | 2 | ||||
100 | 2304 | 48 |
⇒ 1 + | r | = | 50 | = | 25 |
100 | 48 | 24 |
⇒ | r | = | 25 | − 1 = | 1 |
100 | 24 | 24 |
⇒ r = | 100 | = | 25 | = 4 | 1 | % |
24 | 6 | 6 |
Principal = Rs. 2304,
Amount = Rs. 2500
Time = 2 years,
Let Rate % = R %
By using formula,
\( \Large 2500=2304 \left(1+\frac{R}{100}\right)^{2}\)
\( \Large \frac{2500}{2304}= \left(1+\frac{R}{100}\right)^{2}\)
\( \Large \frac{625}{576}= \left(1+\frac{R}{100}\right)^{2}\)
\( \Large\left(\frac{25}{24}\right)^{2} = \left(1+\frac{R}{100}\right)^{2}\)
By taking square root of both sides,
\( \Large \frac{25}{24}= 1+\frac{R}{100} \)
\( \Large \frac{R}{100}=\frac{25}{24}-1 \)
\( \Large R=\frac{100}{24}=\frac{25}{6} \% \)
Rate = \( \Large 4\frac{1}{6} \) %
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Updated On: 27-06-2022
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Text Solution
`4(1)/(2)%``4(1)/(5)%``4(1)/(6)%``4(1)/(3)%`
Answer : C
Answer
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At what rate percent per annum compound interest will 2304 amount to?
Hence, the rate of interest is 461% p.a.
What is the compound interest on rupees 2500 for 2 years at rate of interest for percent per annum?
Detailed Solution 2,500 in 2 years and Rs. 3,000 in 3 years at certain rate of compound interest. ⇒ R = 20% p.a. ∴ Rate of interest is 20% p.a..
At what rate percent per annum compound interest will 5000 amount to 5832 in 2 years?
Hence rate = 8%
What is the amount and the compound interest on 2500 for 2 years at 10% per annum compounded annually?
∴ Amount will be Rs. 3025 and Interest will be Rs. 525 If Compounded Annually.