Question

Find the amount and compound interest on rs 2000 at 10% pa for two and half years, compounded annually

Answer 1

Given:

A sum of Rs. 2000 at 10% pa for two and a half years, compounded annually

To find:

The amount and compound interest

Solution:

We will use the following of compound interest for 2 and a half years to solve the given problem:

• $A = P [1 + \frac{R}{100} ]^2[1 + \frac{\frac{R}{2}}{100} ]$

• $C.I. = A - P$

Here we have,

The sum of money, P = Rs. 2000

The rate of interest, R = 10%

Time period, n = $2\frac{1}{2} \:years$

∴ $A = 2000 [1 + \frac{10}{100} ]^2[1 + \frac{\frac{10}{2} }{100} ]$

$\implies A = 2000 [\frac{110}{100} ]^2[1 + \frac{5 }{100} ]$

$\implies A = 2000 [\frac{110}{100} ]^2[ \frac{105 }{100} ]$

$\implies A = 2000 [1.1 ]^2[1.05 ]$

$\implies A = 2000 [1.21 ][1.05 ]$

$\implies \bold{A = 2541}$ ← the amount

∴ $C.I. = A - P = Rs. 2541 - Rs. 2000 = \bold{Rs. 541}$

Thus, the amount is Rs. 2541 and the compound interest is Rs. 541.

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Answer 2

Answer:

A=₹2541

C.I=₹541

Step-by-step explanation:

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