10,000 for 1 year at 8% per annum compounded half yearly
Answers
Answer:
Compound Interest = 816 Rs.
Step-by-step explanation:
Principal (P) = 10,000 Rs.
Rate (R) = 8%
Time (n)= 1 year
Compound Interest = Amount - Principal
Amount = P(1/1 + R/200)²ⁿ
= 10,000(1/1 + 8/200)² ˣ ¹
= 10,000(1/1 + 8/200)²
= 10,000(200/200 + 8/200)²
= 10,000(208/200)²
= 10,000 × 208/200 × 208/200
= 10,000 × 43,264/40,000
= 432,640,000/40,000
= 10,816 Rs.
Compound Interest = Amount - Principal
= 10,816 - 10,000
= 816 Rs.
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Solution:
Formula:
→ A = P (1 + R/100)^n
→ A = P (1 + 8/100)²
→ 10,000 × (100 + 8²/100)
→ 10,000 = 104²/100²
→ 10,000 × 10816/10,000
→ 1 × 10,816
→ 10,816 - 10,000
→ 186
Know terms:
→ Principal = (P) = 10,000.
→ Rate = (R) = 8%.
→ Time = 1 year.
→ n = number of year.
→ A = amount.
→ CP = cost price.
→ SP = selling price.
→ MP = Marked price.
→ CI = compound interest.
→ SI = simple interest.
Formuls of simple interest:
1) Amount of interest is compounded annually.
→ P (1 + R/100)^n
• Principal , R is rate of interest, n is time period.
2) Amount of interest is compounded half yearly.
→ P (1 + R/200)^2n
• R/2 = half yearly rate.
• 2n = number of half - years.
3) Additional formulas:
• Discount is a reduction given on marked price.
→ Discount = Marked Price - Sale Price.
• Discount can be calculated when discount percentage is given.
→ Discount = Discount % of Marked Price.
Therefore, 186 is the correct answer: