Find difference between CI and SI on RS 5000 for 1 year at 2% PA if the interest is compounDED half yearly
Answers
for simple interest:----
If the sum of Rs. 5000 is put on S.I. for 1 year at 2% p.a. and the same amount, the interest is compounded half-yearly then the difference between the C.I. & S.I. is Rs. 0.5.
Explanation:
Step 1:
For Simple Interest:
Principal, P = Rs. 5000
Time, T = 1 year
Rate of interest, R = 2%
∴ S.I. = [PRT]/100 = [5000*2*1]/100 = Rs. 100
Step 2:
For Compound Interest(Half-yearly):
Principal, P = Rs. 5000
Time, n = 1 year = 2*1 = 2 half-years
Rate of interest, R/2 = 2%/2 = 1%
∴ C.I. = P[(1+R/100)ⁿ - 1]
⇒ C.I. = 5000 [(1+1/100)² - 1]
⇒ C.I. = 5000 [(101/100)² - 1]
⇒ C.I. = 5000 [(10210-10000)/10000]
⇒ C.I. = 5000 * [201/10000]
⇒ C.I. = Rs. 100.5
Step 3:
Thus,
The difference between C.I. and S.I. is,
= Rs. 100.5 – Rs. 100
= Rs. 0.5
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