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A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:
A.Rs. 120
B.Rs. 121
C.Rs. 122
D.Rs. 123
Answers
Given :
A bank offers 5% compound interest calculated on half-yearly basis.
A customer deposits Rs. 1600 each on 1st January and 1st July of a year.
To Find : At the end of the year, the amount he would have gained by way of interest is:
A.Rs. 120
B.Rs. 121
C.Rs. 122
D.Rs. 123
Solution:
Deposited on 1st Jan P = 1600
R = 5 %
Till 1st Jul T = 1/2 year
SI = P * R * T / 100 ( for less than compounding period SI and CI are equal )
SI = Simple Interest
CI = Compound Interest
Interest = 1600 * 5 * (1/2)/100 = Rs 40
Amount on 1st Jul = Deposited on 1st Jan + Interest + Deposited on 1st Jul
=1600 + 40 + 1600
= 3240
P = 3240
R = 5 %
T = 1/2 year ( from 1 st Jul to end of year )
SI = 3240 * 5 * (1/2)/100
= 81 Rs
Total Interest = 40 + 81 = 121 Rs
amount he would have gained by way of interest is Rs 121
Correct option is B. Rs. 121
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Answer:
121 (B)
Step-by-step explanation:
Give datas
Principle = (p) = 1,600
Rate = (R) = 5% = 0.05
Compounded half yearly => [(0.05)/2] = 0.025
Amt = P(1 + i)ⁿ OR CI = P[(1+I)ⁿ-1]
Amt = [1,600(1+0.025)² + 1,600(1+0.025)² ˣ ¹/₂]
Amt = [1,600 × (1.025)² + 1,600(1.025)² ˣ ¹/₂ ]
Amt = 1,681 + 1,640
Amt = 3,321
CI = Amt - Principle
CI = 3,321 - 3,200
CI = 121 (B)