Ashima took a loan of Rs 1,00,000 at 12% p.a. compounded half yearly. She paid Rs 1,12,360. If (1.06)² is equal to 1.1236, then the period for which she took the loan is
(a) 2 years
(b) 1 year
(c) 6 months
(d) 1 1/2 years
Solution:
A loan taken at r% per annum and compounded half yearly will amount to:
A = P(1 + r/200)n
Where P = loan amount
r = 12% per annum
n = number of time periods
A = 1,00,000(1 + 12/200)n
= 1,00,000(1 + 6/100)2
= 1,00,000(1.06)2
Already it is given in the problem statement that (1.06)2 is equal to 1.1236, therefore
A = 1,00,000(1.1236)
= 1,12,360
The period for which Ashima took the loan for one year and that is why the time horizon ‘n’ = 2 because the interest is compounded half yearly.
The applicable rate of interest is r/2 i.e. 12/2 = 6% .
✦ Try This: Ashima took a loan of Rs 1,00,000 at 6% p.a. compounded annually. She paid Rs 1,12,360. If (1.06)2 is equal to 1.1236, then the period for which she took the loan is
The answer is 2 years.
P = 1,00,000
r = 6% compounded annually
n = 2 years
A = 100,000(1 + 6/100)2
= 100,000(1.06)2
= 100,000(1.1236)
= 1,12,360
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 8
NCERT Exemplar Class 8 Maths Chapter 9 Problem 8
Ashima took a loan of Rs 1,00,000 at 12% p.a. compounded half yearly. She paid Rs 1,12,360. If (1.06)² is equal to 1.1236, then the period for which she took the loan is (a) 2 years, (b) 1 year, (c) 6 months, (d) 1 1/2 years
Summary:
Ashima took a loan of Rs 1,00,000 at 12% p.a. compounded half yearly. She paid Rs 1,12,360. If (1.06)² is equal to 1.1236, then the period for which she took the loan is One year
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