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If the sum of 5000 became 6000 in 3 years at a certain rate of compound interest, what will be the sum in 6 years?

a) $7000
b) $8000
c) $9000
d) $10,000

User Tyler Dane
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1 Answer

7 votes

Final answer:

To find the sum in 6 years, we can use the compound interest formula. The sum will be approximately $8344.72.

Step-by-step explanation:

To find the compound interest, we can use the formula:

A = P(1 + r/n)^(nt)

Where:

  • A is the future amount
  • P is the principal amount
  • r is the interest rate
  • n is the number of times interest is compounded per year
  • t is the number of years

Given that the sum of $5000 became $6000 in 3 years, we can plug in the values: A = 6000, P = 5000, r = ?, n = 1, t = 3.

6000 = 5000(1 + r/1)^(1*3)

Dividing both sides by 5000, we get:

1.2 = (1 + r)^3

Taking the cube root of both sides, we get:

1.07177346 = 1 + r

Subtracting 1 from both sides, we get:

r ≈ 0.07177

So the interest rate is approximately 7.18%.

To find the sum in 6 years, we can use the same formula:

A = P(1 + r/n)^(nt)

Substituting the values: P = 6000, r = 0.07177, n = 1, t = 6.

A ≈ 6000(1 + 0.07177/1)^(1*6)

A ≈ $8344.72

Therefore, the sum in 6 years will be approximately $8344.72.

User Paolooo
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