What would be the compound interest on Rupees 8700 at 15 1 by 4% per annum for 2 years compounded annually?

Calculate the compound interest on Rs.5000 for 3 years at 8% per annum compounded annually.

Answer

Hint: To find the amount, we use the formula \[A = P{\left[ {1 + \dfrac{r}{{100}}} \right]^n}\] where, A is the amount, P is principal amount, r is the rate percent yearly and n is the number of years. Since, all the values are known and it is given, hence by substituting the values in the above formula we get the required amount.

Complete step-by-step solution:
Here in this question, we have to find the value of the amount where the number of years, principal amount and the rate is given.
The interest rate per annum, \[r = 8\]
The initial principal amount, \[P = Rs.5000\]
The number of years, \[n = 3\]
We have to find the amount to be paid in case of compound interest
To find the value of amount we have standard formula \[A = P{\left[ {1 + \dfrac{r}{{100}}} \right]^n}\]
Substituting the values to the formula we get,
\[A = 5000{\left[ {1 + \dfrac{8}{{100}}} \right]^3}\]
Take the L.C.M inside the bracket and simplify we get,
\[ \Rightarrow A = 5000{\left[ {\dfrac{{108}}{{100}}} \right]^3}\]
On further simplification.
\[ \Rightarrow A = 5000{\left[ {\dfrac{{27}}{{25}}} \right]^3}\]
On squaring, we get
\[ \Rightarrow A = 5000\left[ {\dfrac{{27 \times 27 \times 27}}{{25 \times 25 \times 25}}} \right]\]
On further simplification.
\[   \Rightarrow A = \dfrac{{5000 \times 27 \times 27 \times 27}}{{15625}} \]
\[  \Rightarrow A = Rs.6298.56 \]
Hence, the amount is 6298.56 rupees. That is, the amount Rs. 6298.56 to be paid at the end of 3 years on Rs. 5000 at 8% per annum compounded annually.
 Therefore the compound interest is determined by
\[C.I = A - P\]
By substituting the values we get
\[ \Rightarrow C.I = 6298.56 - 5000\]
On simplifying we get
\[ \Rightarrow C.I = Rs.1298.56\]

Thus the correct answer is \[ C.I = Rs.1298.56\]

Note: The compound interest is interest calculated on the amount that includes principal and accumulated interest of the previous period whereas simple interest is interest on the invested amount for the entire period. This is the difference between the simple interest and compound interest. To find the value of amount where principal amount, rate of interest and time is known we use the standard formula \[A = P{\left[ {1 + \dfrac{r}{{100}}} \right]^n}\] to determine the value of A. We can also determine the compound interest by subtracting the initial principal amount from the amount.

Find the compound interest on a sum of Rs. 8000 for 3/2 year at a rate of 20%, When the rate is calculated half-yearly.

1. Rs. 5824
2. Rs 2846
3. Rs. 2648
4. Rs. 2864

Answer (Detailed Solution Below)

Option 3 : Rs. 2648

Free

10 Questions 10 Marks 7 Mins

Given:

Sum = Rs. 8000

Time = 3/2 years

Rate = 20%

Concept used:

When the rate is calculated half-yearly,

R becomes R/2.

T becomes 2T.

Formula used:

A = P(1 + R/100)T

C.I. = A - P

Where,

A = Amount, C.I. = Compound interest,

P = Principal or Sum, R = Rate of interest, T = Time

Calculation:

According to the question,

R = 20%/2 = 10%

T = 2 × 3/2 = 3 years

A = P(1 + R/100)T

⇒ A = 8000 × (1 + 10/100)3

⇒ A = 8000 × (11/10)3

⇒ A = 8 × 1331

⇒ A = Rs. 10648

Now,

C.I. = A - P

⇒ C.I. = 10648 - 8000

⇒ C.I. = Rs. 2648

∴ The compound interest is Rs. 2648.

T​ree method for calculation of compound interest

a) When compound interest is calculated for 2 years,

C.I. = 2A + B

b) When compound interest is calculated for 3 years,

C.I. = 3A + 3B + C

c) When compound interest is calculated for 4 years

C.I. = 4A + 6B + 4C + D

A = R% of P

B = R% of A

C = R% fo B

D = R% of C

According to the question,

P = Rs. 8000

R = 10%

T = 3 years

The compound interest for 3 years,

C.I. = 3A + 3B + C      ----(1)

A = 10% of P

⇒ A = 10% of 8000

⇒ A = Rs 800      ----(2)

B = 10% of A

⇒ B = 10% of 800

⇒ B = Rs. 80      ----(3)

C = 10% of B

⇒ C = 10% of 80

⇒ C = Rs. 8      ----(4)

From equation (1) 

C.I. = 3A + 3B + C

Now, put the value of equation (2), (3) and (4)

⇒ C.I. = 3 × 800 + 3 × 80 + 8

⇒ C.I. = 2400 + 240 + 8

⇒ C.I. = Rs. 2648

∴ The compound interest is Rs. 2648.

Last updated on Sep 21, 2022

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