Question

Calculate Amount and Compound Interest ​

Answer 1

General concept:

When the interest accumulated from time to time till now is calculated in the principal amount, then it is called compound interest.

The compund interest can be calculated by using the following formula:

$\boxed{\bf{C.I. = A - P}}$

The amount can be calculated by using the following formula:

$\boxed{\bf{A = P\Bigg[\bigg(1 + \frac{R}{100}\bigg)^{T}\Bigg]}}$

Where,

• CI - Compund Interest
• P - Principal Amount
• R - Rate of Interest
• T - Time Period.

Solution 1:

We have to determine the Amount as well as Compund Interest, when Rs. 645 is principal amount, 4% per annum is rate of interest and 2 years is time period.

According to the given information, we have been given that,

• Principal amount, P = Rs. 645
• Time period, T = 2 years
• Rate of interest, R = 4% p.a
• Amount, A = ?
• Compound interest, CI = ?

By using the amount formula and substituting the given values, we get the following results:

$\implies A = P\Bigg[\bigg(1 + \frac{R}{100}\bigg)^{T}\Bigg] \\ \\ \implies A = 645\Bigg[\bigg(1 + \dfrac{2}{100}\bigg)^{2}\Bigg] \\ \\ \implies A = 645\Bigg[\bigg(\dfrac{100 + 2}{100}\bigg)^{2}\Bigg] \\ \\ \implies A = 645\Bigg[\bigg(\dfrac{102}{100}\bigg)^{2}\Bigg] \\ \\ \implies A = 640\Bigg[\bigg(1.02\bigg)^{2}\Bigg] \\ \\ \implies A = 640\bigg[1.0404\bigg] \\ \\ \implies A = 640 \times 1.0404 \\ \\ \implies \boxed{A = 671.058}$

Now by using the compound interest formula and substituting the known values, we get the following results:

$\implies C.I. = A - P \\ \\ \implies C.I. = 671.058 - 645 \\ \\ \implies \boxed{C.I. = 26.058}$

Hence, the amount is Rs. 671.058 and the compound interest is Rs. 26.058 respectively.

Solution 2:

We have to determine the Amount as well as Compund Interest, when Rs. 100 is principal amount, 10% per annum is rate of interest and 3 years is time period.

According to the given information, we have been given that,

• Principal amount, P = Rs. 1000
• Time period, T = 3 years
• Rate of interest, R = 10% p.a
• Amount, A = ?
• Compound interest, CI = ?

By using the amount formula and substituting the given values, we get the following results:

$\implies A = P\Bigg[\bigg(1 + \frac{R}{100}\bigg)^{T}\Bigg] \\ \\ \implies A = 1000\Bigg[\bigg(1 + \dfrac{10}{100}\bigg)^{3}\Bigg] \\ \\ \implies A = 1000\Bigg[\bigg(\dfrac{100 + 10}{100}\bigg)^{3}\Bigg] \\ \\ \implies A = 1000\Bigg[\bigg(\dfrac{110}{100}\bigg)^{3}\Bigg] \\ \\ \implies A =1000\Bigg[\bigg(\dfrac{11}{10} \bigg)^{3}\Bigg] \\ \\ \implies A = 1000\bigg[\dfrac{1331}{1000} \bigg] \\ \\ \implies A = \cancel{1000}\times \dfrac{1331}{ \cancel{1000}} \\ \\ \implies \boxed{A = 1331}$

Now by using the compound interest formula and substituting the known values, we get the following results:

$\implies C.I. = A - P \\ \\ \implies C.I. = 1331 - 1000 \\ \\ \implies \boxed{C.I. = 331}$

Hence, the amount is Rs. 1331 and the compound interest is Rs. 331 respectively.