Find the amount and the compound interest on Rs.10,000 for 1 whole 1/2 years at 10% per annum compounded half yearly what is this interest be more than the interest he would get if it was compounded annually justify your answer
Answers
Answer:
The amount and the compound interest on ₹ 10,000 for 112 1 1 2 years at 10% per annum, compounded half-yearly is ₹ 11576.25 and ₹ 1576.25 respectively.
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Answer:
rupees 1550
Step-by-step explanation:
A = P[1 + (r/100)]n
P = ₹ 10,000
n = 112" role="presentation" style="box-sizing: inherit; font-family: inherit; margin: 0px; padding: 1px 0px; border: 0px; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; font-size: 15.2px; line-height: 0; vertical-align: baseline; display: inline-block; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">112112 years
R = 10% p.a. compounded annually and half-yearly
where , A = Amount, P = Principal, n = Time period and R = Rate percent
For calculation of C.I. compounded half-yearly, we will take the Interest rate as 5% and n = 3
A = P[1 + (r/100)]n
A = 10000[1 + (5/100)]3
A = 10000[1 + (1/20)]3
A = 10000 × (21/20)3
A = 10000 × (21/20) × (21/20) × (21/20)
A = 10000 × (9261/8000)
A = 5 × (9261/4)
A = 11576.25
Interest earned at 10% p.a. compounded half-yearly = A - P
= ₹ 11576.25 - ₹ 10000 = ₹ 1576.25
Now, let's find the interest when compounded annually at the same rate of interest.
Hence, for 1 year R = 10% and n = 1
A = P[1 + (r/100)]n
A = 10000[1 + (10/100)]1
A = 10000[1 + (1/10)]
A = 10000 × (11/10)
A = 11000
Now, for the remaining 1/2 year P = 11000, R = 5%
A = P[1 + (r/100)]n
A = 11000[1 + (5/100)]
A = 11000[(105/100)]
A = 11000 × 1.05
A = 11550
Thus, compound interest = ₹ 11550 - ₹ 10000 = ₹ 1550
Thus, compound interest = ₹ 11550 - ₹ 10000 = ₹ 1550Therefore, the interest will be less when compounded annually at the same rate