Question

An amount of Rs.10000 becomes Rs.14641 in 2 years, if the interest is compounded half
yearly. What is the rate of compound interest?
a) 25% b) 21% c) 23%
d) 24.5% e) 26.2%

Answer 1

Compound interest accumulation factor :

P (1 + i)ⁿ = Amount

Since it is compounded semiannually :

Time = 2n

Interest = i/2

Amount = 14641

Time = 4

Interest = i/2

Principle = 10000

10000(1 + i/2)⁴ = 14641

1.4641 = (1 + i/2)⁴

(1.4641)^1/4 = 1 + i/2

1.1 = 1 + i/2

2.2 = 2 + i

i = 2.2 - 2

i = 0.2

i = 0.2 × 100 = 20%

Interest :

20%

Answer 2

Answer:

Principal = Rs 10,000

Amount = Rs 14,641

Time = 2 years = 4 half-years

Rate of interest = R% per annum = (R/2)% per six months

10000[ 1 + (R/200)]⁴ = 14641

=> [(200 + R)/200]⁴ = 14641/1000 = (11/10)⁴

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

=> 1 + R/200 = 11/10

=> R/200 = (11/10) — 1 = 1/10

=> R = 200 × 1/10 = 20% per annum

Step-by-step explanation:

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