# 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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