Find the rate at which a sum of money will become four times the origi

1.	Find the rate at which a sum of money will become four times the original amount in 2 years, if the interest is compounded half-yearly.
Answer» Given details are, Time = 2 years = 2×2 = 4 half years Let rate = R % per annum = R/2% half years Let principal be = P So, Amount becomes = 4P By using the formula, A = P (1 + R/100)ⁿ 4P = P (1 + R/2×100)⁴ (1 + R/200)⁴ = 4 (1 + R/200) = 4^1/4 1 + R/200 = 1.4142 R/200 = 1.4142-1 = 0.4142 R = 0.4142 × 200 = 82.84% ∴ Required Rate is 82.84% per annum.

Find the rate at which a sum of money will become four times the original amount in 2 years, if the interest is compounded half-yearly.

Answer»

Given details are,

Time = 2 years = 2×2 = 4 half years

Let rate = R % per annum = R/2% half years

Let principal be = P

So, Amount becomes = 4P

By using the formula,

A = P (1 + R/100)ⁿ

4P = P (1 + R/2×100)⁴

(1 + R/200)⁴ = 4

(1 + R/200) = 4^1/4

1 + R/200 = 1.4142

R/200 = 1.4142-1

= 0.4142

R = 0.4142 × 200

= 82.84%

∴ Required Rate is 82.84% per annum.