Use the formula to solve the problems.
B × In
The amount that results when $6,000 is compounded at 7% annually over eight years=____
The interest earned in this case= ___
To solve the first problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount after time t
P = the principal (initial amount)
r = the annual interest rate (expressed as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
Using the given values:
P = $6,000
r = 7% = 0.07 (expressed as a decimal)
n = 1 (compounded annually)
t = 8 years
Substituting these values into the formula, we have:
A = 6000(1 + 0.07/1)^(1*8)
Simplifying the equation inside the parentheses:
A = 6000(1 + 0.07)^8
Calculating the parentheses first:
A = 6000(1.07)^8
Raising 1.07 to the power of 8:
A ≈ 6000(1.7184)
Multiplying 6000 by 1.7184:
A ≈ $10,310.40
Therefore, the amount that results when $6,000 is compounded at 7% annually over eight years is approximately $10,310.40.
To solve the second problem, the interest earned can be found by subtracting the initial principal from the final amount:
Interest earned = A - P
Substituting in the values we already know:
Interest earned = $10,310.40 - $6,000
Calculating the difference:
Interest earned = $4,310.40
Therefore, the interest earned in this case is $4,310.40.
To solve the first problem, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount after compounding
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case, the principal amount (P) is $6,000, the annual interest rate (r) is 7% or 0.07, and the number of years (t) is 8. However, the formula requires that we know the number of times interest is compounded per year (n). Since the problem does not explicitly mention it, let's assume it is compounded annually, as it is the most common scenario.
Using the formula, we can calculate the final amount after eight years:
A = 6000(1 + 0.07/1)^(1*8)
A = 6000(1.07)^8
A ≈ 6000(1.7171)
A ≈ $10,303.07
Therefore, the amount that results when $6,000 is compounded at 7% annually over eight years is approximately $10,303.07.
To calculate the interest earned, we need to subtract the principal amount from the final amount:
Interest earned = Final amount - Principal amount
Interest earned = $10,303.07 - $6,000
Interest earned ≈ $4,303.07
Therefore, the interest earned in this case is approximately $4,303.07.
Using your formula:
$6000 * .07(8) = ?
However, after the first year, the principal is 6000 + .07(6000) = $6420, so the second year's interest = $6420 * .07(6420) = ?
You need to revise your formula.