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If amount on the principal of Rs 6,000 is written as 6000(1 + 5/100)³ and compound interest payable half yearly, then rate of interest p.a. is _ and time in years is _

Solution:

Amount = Principal(1 + r/100)ⁿ

If the compound interest is payable half yearly, the effective rate of interest is r/2, where,

r = rate of interest per annum

r/2 = 5% --- (1)

Therefore,

r = 10%

Since the interest is compounded half yearly the conversion period is 2n.

Since 2n = 3 --- (2)

n = 3/2 years which is 1 ½ years

Amount = \(6000(1 + \frac{r/2}{100})^{2n}\) --- (3)

Substituting the expressions (1) and (2) in the expression above i.e. (3) we get the desired relation i.e.

Amount = \(6000(1 + \frac{5}{100})^{3}\)

✦ Try this: If the amount on principal of Rs. 8000 is written as 8000(1 + 3/100)⁶ and compound Interest payable quarterly , then rate of interest per annum is __________ and time in years is ____________.

Amount = Principal(1 + r/100)ⁿ

If the compound interest is payable quarterly, the effective rate of interest is r/4, where,

r = rate of interest per annum

r/4 = 3% --- (1)

Therefore,

r = 12%

Since the interest is compounded half yearly the conversion period is 2n.

Since 4n = 6 --- (2)

n = 3/2 years which is 1 ½ years

Amount = \(6000(1 + \frac{r/4}{100})^{2n}\) --- (3)

Substituting the expressions (1) and (2) in the expression above i.e. (3) we get the desired relation i.e.

Amount = \(6000(1 + \frac{3}{100})^{3}\)

If the amount on principal of Rs. 8000 is written as 8000(1 + 3/100)⁶ and compound Interest payable quarterly , then rate of interest per annum is 12% and time in years is one and a half.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 8

NCERT Exemplar Class 8 Maths Chapter 9 Problem 37