5. Calculate the compound interest earned when $15,000 is invested for 6 years at 7% per annum.
To calculate the compound interest earned, we can use the formula:
A = P(1 + r/n)^(nt)
where:
A = the final amount including interest
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years
In this case:
P = $15,000
r = 7% = 0.07
n = annually (compounded once per year)
t = 6 years
Plugging these values into the formula:
A = 15,000(1 + 0.07/1)^(1*6)
A = 15,000(1 + 0.07)^(6)
A = 15,000(1.07)^6
A = 15,000(1.503875)
A ≈ $22,558.13
To find the compound interest earned, we subtract the principal amount from the final amount:
Interest = A - P
Interest = $22,558.13 - $15,000
Interest ≈ $7,558.13
Therefore, the compound interest earned when $15,000 is invested for 6 years at 7% per annum is approximately $7,558.13.
To calculate the compound interest earned, we'll use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = annual interest rate (expressed as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case:
P = $15,000
r = 7% = 0.07 (when expressed as a decimal)
n = 1 (compounded annually)
t = 6 years
Plugging the values into the formula, we get:
A = 15000(1 + 0.07/1)^(1*6)
Now, let's solve it step-by-step.