Calculate compound interest on Rs 4000 for 2.5 years at 8 interest calculated annually

The compound interest on Rs 4000 at 10% per annum for 2 years 3 months compounded annually is A). Rs. 916B). Rs. 900C). Rs. 961D). Rs. 896

Answer

Verified

Hint: First we’ll find the compound interest for 2 years by using its formula. Rest of the 2 months’ interest will be simple because it’s given that the compound interest will be applied annually. In the end, we’ll add both the interest and subtract from the principal amount.Complete step by step solution:
Here, we have given the principal amount (P) as 4000 and interest (r) 10% annually. As we’ll divide the total time duration into two parts because in the time span of 2 years compound interest will be applied and for the rest of the 3 months simple interest will be applied.
The formula for the compound interest is $A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}$
Where A is the total amount, P is the principal amount, r is the rate of interest and n is the time duration.
According to our question, $P=4000, r=10\%, n =2 $years. On Calculation A we get,
\[ A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n} \\
   \Rightarrow A = 4000{\left( {1 + \dfrac{{10}}{{100}}} \right)^2} \\
   \Rightarrow A = P{\left( {1 + \dfrac{1}{{10}}} \right)^2} \\
   \Rightarrow A = 4000{\left( {\dfrac{{11}}{{10}}} \right)^2} \\
   \Rightarrow A = 4000 \times \dfrac{{121}}{{100}} \\
   \Rightarrow A = 4840{\text{ Rs}}{\text{.}} \]
Hence the amount after 2 years will be 4840 and it’ll only work as the principal amount for simple interest. The formula for the simple interest is = $\dfrac{{PRT}}{{100}}$, where P is the principal amount, R is the rate of interest, and T is time spam.
On putting the values, we get,
$ \dfrac{{PRT}}{{100}} \\
   = \dfrac{{4840 \times 10 \times 1}}{{100 \times \times 4}} \\
   = \dfrac{{4840 \times 1 \times 1}}{{10 \times \times 4}} \\
   = \dfrac{{484 \times 1 \times 1}}{{1 \times \times 4}} \\
   = 121 $
So, the total amount after 2 years and 3 months will be Rs 4840 + Rs 121 which is equal to Rs 4961.
Total interest will be = total amount after 2 years 3 months- principal amount
That is, $Rs 4961 – Rs 4000$
And, Rs. 961

Hence, option (c) is the correct option.

Note: Students usually make mistakes in such a type of problem where for some time period compound interest is applied and for some time period, simple interest is applied. It’s always recommended from our side to read the question carefully, especially the interest section. Whether the interest is applied monthly or annually also of which kind, simple of the compound.

Q.

Tick the correct answer in each of the following:

At what rate per cent per annum will a sum of Rs 7500 amount to Rs 8427 in 2 years. Compounded annually ?

(a) 4% (b) 5% (c) 6% (d) 8%

Q.

Tick the correct answer in each of the following:

The value of a machine depreciates at the rate of 20% per annum. It was purchased 2 years ago. If its present value is Rs 40000, for how much was it purchased?

(a) Rs 56000 (b) Rs 62500 (c) Rs 65200 (d) 56500

Q.

Tick the correct answer in each of the following:

The compound interest on Rs 6250 at 8% per annum for 1 year, compounded half yearly, is

(a) Rs 500 (b) Rs 510 (c) Rs 550 (d) Rs 512.50

Q.

Tick the correct answer in each of the following:

The value of a machine depreciates at the rate of 10% per annum. It was purchased 3 years ago for Rs 60000. What is the present value of the machine ?

(a) Rs 53640 (b) Rs 51680 (c) Rs 43740 (d) Rs 43470

Q.

Tick the correct answer in each of the following:

The compound interest on Rs 40000 at 6% per annum for 6 months, compounded quarterly, is

(a) Rs 1209 (b) Rs 1902 (c) Rs 1200 (d) Rs 1306

View More

How do you calculate compound interest for 2.5 years?

What will be the compound interest on 4000 for 2 years at the rate of 5% per annum?

How Do You Solve 2.5 years in simple interest?

What will be the compound interest on Rupees 4000 at 6% per annum for 2 and half years then interest compounded half yearly?