Question

A certain amount of money amounts to 7260 in 2 years and to 7986 in 3 years, interest being compounded annually. Find rate per cent per a number

Answer 1

Answer:

10%

Step-by-step explanation:

Define x:

Let the rate be r

The sum amount to Rs 7260 in 2 years:

P(1 + r)² = 7260

P= 7260/(1 + r)²

The sum amount to Rs 7986 in 3 years:

P(1 + r)³ = 7986

P = 7986/(1 + r)³

Solve r:

7260/(1 + r)² = 7986/(1 + r)³

Cross multiply:

7260(1 + r)³ = 7986(1 + r)²

Subtract 7986(1 + r)² :

7260(1 + r)³ - 7986(1 + r)²  = 0

Take out common factor:

(1 + r)² (7260(1 + r) - 7986) = 0

Evaluate bracket:

(1 + r)² (7260 + 7260r - 7986) = 0  

(1 + r)² (7260r - 726) = 0

Apply zero product property:

(1 + r)² = 0 or (7260r - 726) = 0

r = 0 or 7260r = 726

r = 0 or r = 0.1

Find the rate:  

Rate = 0.1 = 10%

Answer: The rate is 10% p.a.

Answer 2

ANSWER: 10%

★ Assumption:-

→ Let the rate be r

The sum amount to Rs 7260 in 2 years:-

P(1 + r)² = 7260

P = 7260/(1 + r)²

The sum amount to Rs 7986 in 3 years:-

P(1 + r)³ = 7986

P = 7986/(1 + r)³

★ Solving:-

7260/(1 + r)² = 7986/(1 + r)³

★ Cross Multiplying:-

7260(1 + r)³ = 7986(1 + r)²

Now Subtract 7986(1 + r)²

7260(1 + r)³ - 7986(1 + r)² = 0

Take out common factor:

(1 + r)² (7260(1 + r) - 7986) = 0

★ Evaluating:-

(1 + r)² (7260 + 7260r - 7986) = 0

(1 + r)² (7260r - 726) = 0

★ Apply zero product property:-

(1 + r)² = 0 or (7260r - 726) = 0

r = 0 or 7260r = 726

r = 0 or r = 0.1

★ Finding the rate:-

\boxed{\sf{Rate = 0.1 = 10\:percent}}

Rate=0.1=10percent

Hence, the rate is 10% p.a