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प्रश्न
The time taken for ₹ 4400 to become ₹ 4851 at 10%, compounded half yearly is _______
विकल्प
6 months
1 year
`1 1/2` years
2 years
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उत्तर
1 year
Explanation;
Hint:
Principal = ₹ 4400
Amount = ₹ 4851
Rate of interest = 10% p.a
For half yearly, divide by 2,
r = `10/2` = 5%
Compounded half yearly, so the formula is
A = `"P"(1 + "r"/100)^(2"n")`
Substituting in the above formula, we get
4851 = `4400(1 + 5/100)^(2"n")`
4851 = `4400((100 + 5)/100)^(2"n")`
∴ `4851/4400 = (105/100)^(2"n")`
= `(21/20)^(2"n")`
`(21/20)^(2"n") = 4851/4400`
= `(11 xx 441)/(11 xx 400)`
= `441/400`
Taking square root on both sides, we get
`(21/20)^(2"n") = (21/20)^2`
Equating power on both sides
∴ 2n = 2, n = 1
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