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In how many years will a sum of Rs.15625 at 8% pa compounded semi annually become Rs.17,576?
- a)2(1/3)yrs
- b)2yrs
- c)1(1/2)yrs
- d)1yr
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
In how many years will a sum of Rs.15625 at 8% pa compounded semi annu...
15625*(1+(4/100))2n = 17576
15625*(104/100)2n = 17576
(26/25)2n = 17576/15625 = (26/27)3
2n = 3 N =3/2 = 1(1/2) yrs
15625*(104/100)2n = 17576
(26/25)2n = 17576/15625 = (26/27)3
2n = 3 N =3/2 = 1(1/2) yrs
Most Upvoted Answer
In how many years will a sum of Rs.15625 at 8% pa compounded semi annu...
Explanation :
15625 x (1+(4/100))2n = 17576
15625 x (104/100) 2n = 17576
(26/25) 2n = 17576/15625 = (26/27)3
2n = 3
N =3/2 = 1(1/2) yrs
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Community Answer
In how many years will a sum of Rs.15625 at 8% pa compounded semi annu...
Given:
Principal amount (P) = Rs. 15625
Rate of interest (R) = 8% per annum
Time period (T) = ?
Compound interest (CI) = Rs. 1951 (Rs. 17576 - Rs. 15625)
Formula Used:
Compound Interest = P(1 + R/100)^n - P
Where,
n = number of compounding periods
Calculation:
As the interest is compounded semi-annually, the time period will be in half-years.
Let the time period be 'n' half-years.
So, the number of compounding periods (n) will be 2n.
Using the formula of compound interest, we can find the value of 'n' as follows:
CI = P(1 + R/100)^n - P
1951 = 15625(1 + 8/100)^(2n) - 15625
(1 + 0.08)^(2n) = (1951 + 15625)/15625
(1.08)^(2n) = 1.125
2n log(1.08) = log(1.125)
n = log(1.125) / (2 log(1.08))
n = 3/4 year
Therefore, the time period (T) in years will be:
T = n/2 = (3/4)/2 = 3/8 year
Converting the time period into months, we get:
T = 3/8 * 12 = 4.5 months
Hence, the answer is 1(1/2) years.
Principal amount (P) = Rs. 15625
Rate of interest (R) = 8% per annum
Time period (T) = ?
Compound interest (CI) = Rs. 1951 (Rs. 17576 - Rs. 15625)
Formula Used:
Compound Interest = P(1 + R/100)^n - P
Where,
n = number of compounding periods
Calculation:
As the interest is compounded semi-annually, the time period will be in half-years.
Let the time period be 'n' half-years.
So, the number of compounding periods (n) will be 2n.
Using the formula of compound interest, we can find the value of 'n' as follows:
CI = P(1 + R/100)^n - P
1951 = 15625(1 + 8/100)^(2n) - 15625
(1 + 0.08)^(2n) = (1951 + 15625)/15625
(1.08)^(2n) = 1.125
2n log(1.08) = log(1.125)
n = log(1.125) / (2 log(1.08))
n = 3/4 year
Therefore, the time period (T) in years will be:
T = n/2 = (3/4)/2 = 3/8 year
Converting the time period into months, we get:
T = 3/8 * 12 = 4.5 months
Hence, the answer is 1(1/2) years.
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