Answer:
look at solution
Explanation:
To find the interest earned on $15,000 invested for 7 years at 7% interest compounded differently, we can use the formula for compound interest:
A = P(1 + r/n)^(nt) - P
Where:
A = the total amount after interest
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
a. Annually:
For compounding annually, the interest is compounded once a year. So in this case, n = 1.
Using the formula, we have:
A = 15,000(1 + 0.07/1)^(1*7) - 15,000
b. Semiannually (twice a year):
For compounding semiannually, the interest is compounded twice a year. So in this case, n = 2.
Using the formula, we have:
A = 15,000(1 + 0.07/2)^(2*7) - 15,000
c. Quarterly:
For compounding quarterly, the interest is compounded four times a year. So in this case, n = 4.
Using the formula, we have:
A = 15,000(1 + 0.07/4)^(4*7) - 15,000
d. Monthly:
For compounding monthly, the interest is compounded twelve times a year. So in this case, n = 12.
Using the formula, we have:
A = 15,000(1 + 0.07/12)^(12*7) - 15,000
e. Continuously:
For continuous compounding, we use the formula:
A = P*e^(rt)
Where e is the mathematical constant approximately equal to 2.71828.
Using the formula, we have:
A = 15,000*e^(0.07*7) - 15,000
Now, you can use these formulas to calculate the interest earned in each scenario.