Find the rate percent per annum if Rs. 2000 amount to Rs. 2662 in 1 ½

1.	Find the rate percent per annum if Rs. 2000 amount to Rs. 2662 in 1 ½ years, interest being compounded half-yearly?
Answer» Given details are, Principal = Rs 2000 Amount = Rs 2662 Time = 1 ½ years = 3/2 × 2 = 3 half years Let rate be = R% per annum = R/2 % half yearly By using the formula, A = P (1 + R/100)ⁿ 2662 = 2000 (1 + R/2×100)³ (1 + R/200)³ = 1331/1000 (1 + R/100)³ = (11/10)³ By cancelling the powers on both sides, (1 + R/200) = (11/10) R/200 = 11/10 – 1 = (11-10)/10 = 1/10 R = 200/10 = 20% ∴ Required Rate is 20% per annum.

Find the rate percent per annum if Rs. 2000 amount to Rs. 2662 in 1 ½ years, interest being compounded half-yearly?

Answer»

Given details are,

Principal = Rs 2000

Amount = Rs 2662

Time = 1 ½ years = 3/2 × 2 = 3 half years

Let rate be = R% per annum = R/2 % half yearly

By using the formula,

A = P (1 + R/100)ⁿ

2662 = 2000 (1 + R/2×100)³

(1 + R/200)³ = 1331/1000

(1 + R/100)³ = (11/10)³

By cancelling the powers on both sides,

(1 + R/200) = (11/10)

R/200 = 11/10 – 1

= (11-10)/10

= 1/10

R = 200/10

= 20%

∴ Required Rate is 20% per annum.