An amount of INR 10, 000 is added every year at rate of interest 10% per annum, interest being compounded yearly. What is the difference between amount earned in 4th year and amount earned in 3rd year. 

An amount of INR 10, 000 is added every year at rate of interest 10% per annum, interest being compounded yearly. What is the difference between amount earned in 4th year and amount earned in 3rd year.  Correct Answer 1089

Formula used:

(i) P(1 + (R / n))^nt

Calculations:

Now, amount of 10, 000 is added every year and interest is compounded yearly

Hence amount earned in fourth year = Total amount earned till four years – Total amount earned till 3 years

⇒ 10000((1.1) + (1.1)² + (1.1)³ + (1.1)⁴) – 10000((1.1) + (1.1) ² + (1.1)³)

⇒ 10000(1.1) ((1 + (1.1) + (1.1) ² + (1.1) ³) – 10000(1.1) (1 + (1.1) + (1.1)²)

⇒ 11000(1 + (1.1) + (1.21) + (1.331)) – 11000(1 + (1.1) + (1.221))

⇒ 11000(4.641) – 11000(3.321)

Amount earned in fourth year = 14520

Now,

Amount earned in third year = 10000 ((1.1) + (1.1)² + (1.1)³) – 10000 ((1.1) + (1.1)²)

⇒ 10000(1.1) (1 + (1.1) + (1.1)²) – 10000(1.1) (1 + (1.1))

⇒ 11000(1 + (1.1) + (1.221)) – 11000(1 + 1.1)

⇒ 11000 (3.321) – 11000 (2.1)

⇒ 11000 (1.221)

⇒ 13431

i.e,

Amount earned in third year = 13431

Amount earned in fourth year – Amount earned in third year = 14520 – 13431

i.e, 1089