Question

A sum amounts to 6600 in 1 year and 7986 in 3 years at compound interest . find the rate and the sun .​

Answer 1

Given :

• A sum amounts to 6600 in 1 year and 7986 in 3 years at compound interest . find the rate and the sum.

Find :

• Find the rate and the sum.

Solution :

• The compound interest accumulation formula is given by :

❒ A = P(1 + i)ⁿ

❒ P = Principal Amount

❒ I = Rate of Interest

❒ n = Time Period

• Substituting this in each of the cases we have :

❖ 6600 = P(1 + i)

❖ 7986 = P(1 + i)³

• Rewrite the equations we have :

☯ P = 6600/(1 + i)

☯ P = 7986/(1 + i)³

• Equating the two values of P we have :

↦ 6600/(1 + i) = 7986/(1 + i)³

↦(1 + i)³/(1 + i) = 7986/6600

↦(1 + i)² = 1.21

• Getting square root on both sides we have :

⟹ 1 + i = 1.1

⟹ i = 1.1 - 1

⟹ i = 0.10

⟹ i = 10%

• Substituting the value of in any of the equations to get P, We have :

➮ 6600/(1.10)

➮ 6000

Therefore,

• The sum is Rs.6000 and the rate of percent is 10%.

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