Question

The time taken for ₹ 4400 to become ₹ 4851 at 10%, compounded half yearly is _______

Options

• 6 months

• 1 year

• `1 1/2` years

• 2 years

Answer 1

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