in how many years will rupees 3375 amounts to Rupees 4096 at 20 upon 3% per annum interest is compound annually
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Answer:
ow many years will Rs 3375 become Rs 4096 at 13 1/3 % p.a where interest is compounded half yearly
Report by AdvikaRai5320 19.10.2019
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ananya6170
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BhagyashreechowdhuryAce
Answer:
Principal, P = Rs. 3375
Amount, A = Rs. 4096
Since it is compounded on a half-yearly basis, so,
Let the time period be “n” half years.
And the rate of interest, R = R/2 = ½ * 13\frac{1}{3} = \frac{20}{3}%
The formula for calculating the amount in compound interest is given as,
A = P [1+ R/100]ⁿ
Substituting the given values, we get
4096 = 3375 [1+ (20/300)]ⁿ
⇒ 4096/3375 = [1 + 2/30]ⁿ
⇒ 1.21 = [32/30]ⁿ
Taking log on both sides
⇒ log 1.21 = log (1.06)ⁿ
⇒ log 1.21 = n log 1.06 ….. [since log aᵇ = b log a]
⇒ 0.0827 = n * 0.0253
⇒ n = 0.0827/0.0253
⇒ n = 3.2 ≈ 3 half years
We got n = 3 half years, therefore,
The required time period will be = 3/2 years = 1.5 years .
Thus, in 1.5 years Rs. 3375 become Rs. 4096 at 13 \frac{1}{3}% p.a. where the interest is compounded half-yearly.