avi took a loan of rs. 50000 from the bank at a rate of 15%.find the compound interest after 2 years when the interest is :
(A)compounded half yearly
Answers
Principal, P = Rs. 50000
Rate of interest, R = 10% p.a.
Time period, n = 1 ½ years
Let the amount he would be repaid be denoted as “A”.
Case (a): Interest is compounded annually
A = P [1 + \frac{R}{100}
100
R
ⁿ
Substituting the above-given values in the formula
⇒ A = 50000 [1+ \frac{10}{100}
100
10
]^1 ½
⇒ A = 50000 [1+\frac{10}{100}
100
10
] [1+ \frac{\frac{10}{2}}{100}
100
2
10
⇒ A = 50000 * \frac{11}{10}
10
11
* \frac{21}{20}
20
21
⇒ A = Rs. 57750
Thus, the amount Anuj is repaid when the interest is compounded annually is Rs. 57750.
Case (b): Interest is compounded half-yearly
Here
R = 10/2 = 5%
Time = 2n = 2 * (3/2) = 3 years
Now,
A = P [1+ \frac{R}{100}
100
R
²ⁿ
Substituting the above-given values in the formula
⇒ A = 50000 [1+ \frac{5}{100}
100
5
]³
⇒ A = 50000 * [\frac{21}{20}
20
21
]³
⇒ A = \frac{ < /strong > 50000*21*21*21 < strong > }{ < /strong > 20*20*20 < strong > }
</strong>20∗20∗20<strong>
</strong>50000∗21∗21∗21<strong>
⇒ A = Rs. 57881.25
Thus, the amount Anuj is repaid when the interest is compounded half-yearly is Rs. 57881.25.
Answer:
Principal, P = Rs. 50000
Rate of interest, R = 10% p.a.
Time period, n = 1 ½ years
Let the amount he would be repaid be denoted as “A”.
Case (a): Interest is compounded annually
A = P [1 + \frac{R}{100}
100
R
ⁿ
Substituting the above-given values in the formula
⇒ A = 50000 [1+ \frac{10}{100}
100
10
]^1 ½
⇒ A = 50000 [1+\frac{10}{100}
100
10
] [1+ \frac{\frac{10}{2}}{100}
100
2
10
⇒ A = 50000 * \frac{11}{10}
10
11
* \frac{21}{20}
20
21
⇒ A = Rs. 57750
Thus, the amount Anuj is repaid when the interest is compounded annually is Rs. 57750.
Case (b): Interest is compounded half-yearly
Here
R = 10/2 = 5%
Time = 2n = 2 * (3/2) = 3 years
Now,
A = P [1+ \frac{R}{100}
100
R
²ⁿ
Substituting the above-given values in the formula
⇒ A = 50000 [1+ \frac{5}{100}
100
5
]³
⇒ A = 50000 * [\frac{21}{20}
20
21
]³
⇒ A = \frac{ < /strong > 50000*21*21*21 < strong > }{ < /strong > 20*20*20 < strong > }
</strong>20∗20∗20<strong>
</strong>50000∗21∗21∗21<strong>
⇒ A = Rs. 57881.25
Thus, the amount Anuj is repaid when the interest is compounded half-yearly is Rs. 57881.25.