At what rate percent per annum will a sum of rs 2000 amount to Rs 2315.25 in 3 years

According to the question, compounded half yearly

Rate = \( \Large \frac{R}{2} \)

Time =\( \Large \frac{2T}{3} \)

Amount=\( \Large P \left(1+\frac{R}{2 \times 100}\right)^{3}\)

2315.25=\( \Large 2000 \left(1+\frac{R}{200}\right)^{3}\)

\( \Large \frac{2315.25}{2000}= \left(1+\frac{R}{200}\right)^{3}\)

\( \Large \frac{231525}{200000}= \left(1+\frac{R}{200}\right)^{3}\)

\( \Large \frac{9261}{8000}= \left(1+\frac{R}{200}\right)^{3}\)

\( \Large\left(\frac{21}{20}\right)^{3} = \left(1+\frac{R}{200}\right)^{3}\)

\( \Large 1+\frac{R}{200}=\frac{21}{20}=R = 10\% \)

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Given:

Compound interest on Rs.2000 for 3 years = Rs.315.25 

Formulas used:

Amount = Principal + Interest 

Amount = P(1 + r/100)n

Calculation:

Amount = 2000 + 315.25 = Rs.2315.25 

Amount = P(1 + r/100)n

⇒ 2315.25 = 2000(1 + r/100)3

⇒ 231525/200000 = (1 + r/100)3

⇒ ∛9261/8000 = 1 + r/100 

⇒ 21/20 - 1 = r/100 

⇒ (21 - 20)/20 = r/100 

⇒ 1/20 = r/100 

⇒ 1 = r/5 

⇒ r = 5 

∴ The rate of interest is 5% per annum.

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Find the rate percent per annum, if Rs 2000 amount to Rs 2315.25 in an year and a half, interest being compounded six monthly.

Let the rate percent per annum be R.
Because interest is compounded every six months, n will be 3 for 1.5 years.
Now, 
\[A = P \left( 1 + \frac{R}{200} \right)^n \]
\[2, 315 . 25 = 2, 000 \left( 1 + \frac{R}{200} \right)^3 \]
\[ \left( 1 + \frac{R}{200} \right)^3 = \frac{2, 315 . 25}{2, 000}\]
\[ \left( 1 + \frac{R}{200} \right)^3 = 1 . 157625\]
\[ \left( 1 + \frac{R}{200} \right)^3 = \left( 1 . 05 \right)^3 \]
\[1 + \frac{R}{200} = 1 . 05\]
\[\frac{R}{200} = 0 . 05\]
\[ = 10\]
Thus, the required rate is 10 % per annum.


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`5%``7%``12%``15%`

Answer : C

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At what rate percent per annum will a sum of rs 2000 amount to Rs 2315.25 in 3 years

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At what rate per annum will Rs 2000 becomes Rs 2205 in 2 years compounded annually?

⟹r=0. 05=5%

At what rate percent per annum of compound interest will Rs 2000 amounts to Rs 2332.8 in 2 years?

This is Expert Verified Answer Given, Principal = 2000, A = 2332.80, Time n = 2 years. ⇒ r = 8. Therefore, R = 8%.

In what time will Rs 2000 amounts to Rs 2315.25 at 5% per annum compounded annually?

Given A = 2000, P = 2315.25, n = 3 years. r = 5%. Therefore the required rate is 5% per annum.

At what rate percent per annum will Ron lends a sum of 2000?

Hence, the rate of interest will be equal to 5%.