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.