Question
$3000 principal earnings 5 percent compound annually, four years
Answers
GPT 3.5
To find the compound interest earned on a $3000 principal at a 5% annual interest rate over a period of four years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (in this case, $3000)
r = the annual interest rate (expressed as a decimal, in this case 0.05)
n = the number of times that interest is compounded per year (since the question does not specify, we assume it is compounded annually, so n = 1)
t = the number of years the money is invested/loaned for (in this case, 4 years)
Plugging in the values into the formula:
A = 3000(1 + 0.05/1)^(1*4)
A = 3000(1 + 0.05)^4
A = 3000(1.05)^4
A = 3000(1.21550625)
A = 3646.52
Therefore, the future value of the investment/loan after four years would be $3646.52.
To calculate the compound interest earned, we can subtract the principal from the future value:
Compound interest earned = A - P
Compound interest earned = 3646.52 - 3000
Compound interest earned = 646.52
Therefore, the compound interest earned on a $3000 principal at a 5% annual interest rate over a period of four years would be $646.52.
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (in this case, $3000)
r = the annual interest rate (expressed as a decimal, in this case 0.05)
n = the number of times that interest is compounded per year (since the question does not specify, we assume it is compounded annually, so n = 1)
t = the number of years the money is invested/loaned for (in this case, 4 years)
Plugging in the values into the formula:
A = 3000(1 + 0.05/1)^(1*4)
A = 3000(1 + 0.05)^4
A = 3000(1.05)^4
A = 3000(1.21550625)
A = 3646.52
Therefore, the future value of the investment/loan after four years would be $3646.52.
To calculate the compound interest earned, we can subtract the principal from the future value:
Compound interest earned = A - P
Compound interest earned = 3646.52 - 3000
Compound interest earned = 646.52
Therefore, the compound interest earned on a $3000 principal at a 5% annual interest rate over a period of four years would be $646.52.