question 1
compound interest at 5 % per annum is charged on Rs. 1000. The principal for the second year is
question 2
if the interest is payable quaterly , after what time will Rs. 1600 amount to Rs. 1852.20 at 20 % per annum
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Answers
answer : Q1 : 1050 Rs. Q2 : 9 months
1. principal for the second year = P + CI for first year
= P + [P(1 + r/100)¹ - P]
here, given P = 1000 and r = 5 % per annum.
= 1000 + [1000 + 1000 × 5/100 - 1000]
= 1000 + 50
= 1050 Rs.
2. rate of interest , r = 20% per annum
so, rate of interest , r'= 20/4 = 5 % per quarterly.
principal, P = 1600 Rs.
and Amount after time t, A = 1852.2 Rs.
using formula, A = P(1 + r'/100)⁴ⁿ
1852.2 = 1600(1 + 5/100)⁴ⁿ
⇒1852.2/1600 = (1 + 0.05)⁴ⁿ
⇒1.157625 = (1.05)⁴ⁿ
we know, (1.05)³ = 1.157625
so, 1.157625 = (1.05)³ = (1.05)⁴ⁿ
⇒4n = 3
⇒n = 3/4 year = 9 months
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