Question

In how many years will ₹ 3375 become ₹ 4096 at `13 1/3` p.a if the interest is compounded half-yearly?

Answer 1

Principal = ₹ 3375

Amount = ₹ 4096

r = `13 1/3%  "p.a"`

= `40/3%  "p.a"`

Compounded half-yearly r = `(40/3)/2 = 20/3%` half-yearly

Let no. of years be n

For compounding half-yearly, formula is

A = `"P"(1 + "r"/100)^(2"n")`

∴ 4096 = `3375 + (1 + (20/3)/100)^(2"n")`

∴ `4096/3375 = (1 + 20/(3 xx 100))^(2"n")`

= `(1 + 1/15)^(2"n")`

`((15 + 1)/15)^(2"n") = (16/15)^(2"n")`

⇒ `4096/3375 = (16/15)^(2"n")`

Taking cubic root on both sides,

`(16/15)^((2"n")/3) = root(3)(4096)/(root(3)(3375)) = 16/15`

∴ `(2"n")/3` = 1

∴ n = `3/2` = 1.5 years