Use the formula to solve the problems.
B * In
The amount that results when $3,000 is compounded at 7% annually over eight years.
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The interest earned in this case.
To solve these problems, we need to use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
Where:
A = the final amount
P = the initial principal (the amount of money initially invested)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
Let's solve each problem step by step:
1. The amount that results when $3,000 is compounded at 7% annually over eight years:
In this case:
P = $3,000
r = 7% = 0.07 (convert the percentage to decimal)
n = 1 (since interest is compounded annually)
t = 8
Plug these values into the formula:
A = $3,000 * (1 + 0.07/1)^(1*8)
Simplify:
A = $3,000 * (1 + 0.07)^8
A = $3,000 * (1.07)^8
Use a calculator to calculate (1.07)^8, which equals approximately 1.718223
A = $3,000 * 1.718223
A = $5,154.67 (rounded to two decimal places)
Therefore, the amount resulting from compounding $3,000 at 7% annually over eight years is approximately $5,154.67.
2. The interest earned in this case:
Interest earned can be calculated by subtracting the initial principal, P, from the final amount, A:
Interest = A - P
Using the final amount A calculated in the previous problem ($5,154.67) and the initial principal P ($3,000):
Interest = $5,154.67 - $3,000
Interest = $2,154.67
Therefore, the interest earned in this case is $2,154.67.