At what rate per cent per annum will 640 amount to 774.40 in 2 years when compounded annually?

At what rate percentage a sum of \[Rs.640\] be compounded to \[Rs.774.40\] in two years?

Inhaltsverzeichnis Show

At what rate percentage a sum of \[Rs.640\] be compounded to \[Rs.774.40\] in two years?
What is the rate of compound interest per annum 640?
In what time will ₹ 1800 amount to ₹ 2178 at 10% per annum compounded annually?
At what rate percent per annum will a sum of 2000 amount to 2205 in 2 years compounded annually?
At what rate percent per annum will ₹ 8000 produce ₹ 400 interest in 2 years?

Answer

Verified

Hint: In this question, we have to find the rate percentage at which it was compounded that we reached the given amount in two years. We do this by using the formula of Amount in terms of Principle, Time and Rate percentage. On solving the formula \[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}\] we will get the desired result.

Formula used: If \[P\] is the principal money at the starting, which is compounded for \[n\] years at the rate of \[r\] percentage, the total amount we will reach is given by,
\[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}\].

Complete step-by-step answer:
In this question, we are given principal rupees which get compounded to amount rupees given above in two years. We have to find the rate percentage at which it was compounded that we reached the given amount in two years. So,
Principle money, \[P = Rs.640\]
Amount, \[A = Rs.774.40\]
Time compounded in years, \[n = 2\]
Let rate percentage \[ = r\]
We know that Amount in terms of Principle, Time and Rate percentage is given by,
\[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}\]
On putting the values from above,
\[
   \Rightarrow 774.40 = 640{\left( {1 + \dfrac{r}{{100}}} \right)^2} \\
   \Rightarrow \dfrac{{774.40}}{{640}} = {\left( {1 + \dfrac{r}{{100}}} \right)^2} \\
\]
\[\dfrac{{774.40}}{{640}}\] can also be written as \[{\left( {\dfrac{{11}}{{10}}} \right)^2}\]. Using this in the above step,
\[
   \Rightarrow {\left( {\dfrac{{11}}{{10}}} \right)^2} = {\left( {1 + \dfrac{r}{{100}}} \right)^2} \\
   \Rightarrow \dfrac{{11}}{{10}} = 1 + \dfrac{r}{{100}} \\
\]
On further solving the above step,
\[
   \Rightarrow \dfrac{{11}}{{10}} - 1 = \dfrac{r}{{100}} \\
   \Rightarrow \dfrac{1}{{10}} = \dfrac{r}{{100}} \\
   \Rightarrow r = \dfrac{{100}}{{10}} \\
   \Rightarrow r = 10 \\
\]
Hence, \[r = 10\% \], we compounded \[Rs.640\] to \[Rs.774.40\] in two years.

Note: In above question it is to note if the principle is compounded annually for two years or the principle is compounded in two yearly basis. In this case it is the former one. In compound interest, we get interest on the in interest as well, Amount in compound interest is more than amount in simple interest form.

Free

10 Questions 15 Marks 7 Mins

Given:

Principal = Rs 640

Amount = Rs 774.40

Time = 2 years

Concept:

A = P (1 + R/100)n

Calculation:

Let rate = R%

By using the formula,

⇒ A = P (1 + R/100)n

⇒ 774.40 = 640 (1 + R/100)2

⇒ (1 + R/100)2 = 774.40/640

⇒ (1 + R/100)2 = 484/400

⇒ (1 + R/100)2 = (22/20)2

⇒ By cancelling the powers on both sides, (1 + R/100) = (22/20)

⇒ R/100 = 22/20 – 1 = (22 - 20)/20 = 2/20

⇒ R = 100/10 = 10%

∴ Required Rate is 10% per annum.

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