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Find the ratio of the compound interest received on a certain principal, if parked for 4 years at 12% p.a. rate of interest, compounded half yearly to the simple interest that can be received if the same sum is invested for 6 years at 9% per annum
  • a)
    0.95
  • b)
    1.0
  • c)
    1.05
  • d)
    1.1
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Find the ratio of the compound interest received on a certain princip...
Given:
Principal amount = P
Rate of interest = 12% per annum
Time period = 4 years
Rate of compounding = half yearly

Formula for compound interest:
Compound Interest = P * (1 + r/n)^(nt) - P

Where:
P = Principal amount
r = Rate of interest per period
n = Number of compounding periods per year
t = Time period in years

Step 1: Calculate the compound interest for the given principal amount for 4 years at 12% p.a. rate of interest when compounded half yearly.
P = P
r = 12%/2 = 6% per half year (converted to half yearly rate)
n = 2 (compounded half yearly)
t = 4 years

Compound Interest = P * (1 + r/n)^(nt) - P
CI1 = P * (1 + 6%/2)^((2)(4)) - P

Step 2: Calculate the simple interest for the same principal amount for 6 years at 9% per annum.
P = P
r = 9% per annum
t = 6 years

Simple Interest = P * r * t
SI = P * 9% * 6

Step 3: Calculate the ratio of compound interest to simple interest.
Ratio = CI1 / SI

Step 4: Simplify the ratio.
Ratio = {P * (1 + 6%/2)^((2)(4)) - P} / {P * 9% * 6}
Ratio = {(1.06)^8 - 1} / 0.54

Calculating the value of (1.06)^8 and substituting it in the ratio formula:
Ratio = (1.593848 - 1) / 0.54
Ratio = 0.593848 / 0.54
Ratio ≈ 1.099675

Therefore, the ratio of the compound interest received on the certain principal, if parked for 4 years at 12% p.a. rate of interest, compounded half yearly to the simple interest that can be received if the same sum is invested for 6 years at 9% per annum is approximately 1.1, which is option D.
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Community Answer
Find the ratio of the compound interest received on a certain princip...
Let the Principal amount be P
CI = P (1+ 0.06)8 - P (4 years constitute 8 half year periods)
= P [(1.06)8 - 1]
= P [1.5938 - 1] = P*0.5938
SI = (P * 9 * 6)/ 100 = 0.54P
Ratio= 0.5938P/0.54P = 0.5938/0.54 = 1.1
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Find the ratio of the compound interest received on a certain principal, if parked for 4 years at 12% p.a. rate of interest, compounded half yearly to the simple interest that can be received if the same sum is invested for 6 years at 9% per annuma)0.95b)1.0c)1.05d)1.1Correct answer is option 'D'. Can you explain this answer?
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