Question

A certain sum of money amounts to 7260 in 2years and to 7986in 3 years,interest being compounded quarterly find rate percent per annum ​

Answer 1

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$\boxed{\sf{→10\:percent}}$

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★ 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:-

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

Hence, the rate is 10% p.a

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Answer 2

A certain sum of money amounts to 7260 in 2years and to 7986in 3 years,interest being compounded annually. Find rate percent and sum

Answer : 10,

6000

Step by step explanation:

Clearly, the interest on Rs 7260 for 1 year =Rs(7986 -7260)= Rs726

Rate of interest =(100×726/7260×1)%p.a =10%p.a

Let the sum be Rs x. then,

x × (1+10/100)^2 =7260

=> x × 11/10 ×11/10 =7260

=> x = (7260 × 100/121)

=> x =6000

•

• • Rate =10%

Sum = 6000