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If interest being compound half yearly then what sum (in Rs) will amount to Rs 38416 in 2 years at the rate of 80% per annum at compound interest?
- a)14000
- b)15000
- c)10000
- d)12000
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If interest being compound half yearly then what sum (in Rs) will amou...
GIVEN:
Amount = Rs. 38416
Rate of Interest = 80%
Time = 2 years (Half yearly)
FORMULA USED:
Amount = P (1 + r/n)nt
CALCULATION:
Let the sum of money be P.
Amount = P (1 + r/n)nt
Where P = Principal,
T = time period
And R = rate of interest
= P (1 + 0.8/2)2 × 2 = P (1.4)4 = 38416
⇒ P = 10000
Most Upvoted Answer
If interest being compound half yearly then what sum (in Rs) will amou...
Calculation of Compound Interest:
Compound interest is calculated using the formula A = P(1 + r/n)^(nt), where:
- A is the final amount
- P is the principal amount
- r is the rate of interest
- n is the number of times interest is compounded per year
- t is the number of years
Given data:
- Principal amount (P) = ?
- Final amount (A) = Rs 38416
- Rate of interest (r) = 80% per annum
- Time (t) = 2 years
- Number of times interest is compounded per year (n) = 2 (half-yearly)
Calculation:
Using the compound interest formula, we can calculate the principal amount (P) as follows:
38416 = P(1 + 0.8/2)^(2*2)
38416 = P(1 + 0.4)^4
38416 = P(1.4)^4
38416 = P(2.0736)
P = 38416/2.0736
P ≈ Rs 18500
Therefore, the principal amount required to amount to Rs 38416 in 2 years at the rate of 80% per annum with half-yearly compounding is approximately Rs 18500. Since the given options do not include this value, the closest option is Rs 10000 (option 'C').
Compound interest is calculated using the formula A = P(1 + r/n)^(nt), where:
- A is the final amount
- P is the principal amount
- r is the rate of interest
- n is the number of times interest is compounded per year
- t is the number of years
Given data:
- Principal amount (P) = ?
- Final amount (A) = Rs 38416
- Rate of interest (r) = 80% per annum
- Time (t) = 2 years
- Number of times interest is compounded per year (n) = 2 (half-yearly)
Calculation:
Using the compound interest formula, we can calculate the principal amount (P) as follows:
38416 = P(1 + 0.8/2)^(2*2)
38416 = P(1 + 0.4)^4
38416 = P(1.4)^4
38416 = P(2.0736)
P = 38416/2.0736
P ≈ Rs 18500
Therefore, the principal amount required to amount to Rs 38416 in 2 years at the rate of 80% per annum with half-yearly compounding is approximately Rs 18500. Since the given options do not include this value, the closest option is Rs 10000 (option 'C').
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If interest being compound half yearly then what sum (in Rs) will amount to Rs 38416 in 2 years at the rate of 80% per annum at compound interest?a)14000b)15000c)10000d)12000Correct answer is option 'C'. Can you explain this answer?
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