Use the compound interest formula
A=p(1+r/n)nt
to compute the total
amount of the investment if $7500 is invested at 9% compounded monthly for
4 years.
The "nt" in your equation is an exponent and should be written ^nt, since we can only write numbers on a single line here. n is the number of interest-componding periods in a year (12), at t is the number of years (4).
In your case, r/n = 9%/12 = .0075, and nt = 48
Therefore A = 7500(1.0075)^48
= 7500*1.4314053
= 10,733.54
I used a hand calculator to take the 48th power of 1.0075.
Thanks a lot
To compute the total amount of the investment using the compound interest formula, you will need to substitute the given values into the formula:
A = P(1 + r/n)^(nt)
Where:
A = total amount of the investment
P = principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
Given:
P = $7500
r = 9% = 0.09 (converted to decimal form)
n = 12 (compounded monthly)
t = 4 years
Substituting the values into the formula:
A = 7500(1 + 0.09/12)^(12*4)
Now, let's simplify this expression:
A = 7500(1 + 0.0075)^(48)
A = 7500(1.0075)^(48)
Next, calculate the value inside the parentheses:
(1.0075)^48 ≈ 1.430646733
Now, multiply the principal amount by the calculated value:
A ≈ 7500 * 1.430646733
A ≈ 10,729.85
Therefore, the total amount of the investment after 4 years, compounded monthly at a 9% interest rate, will be approximately $10,729.85.
To compute the total amount of the investment using the compound interest formula, we need to substitute the given values into the formula:
A = P(1 + r/n)^(nt)
Where:
A = Total amount of the investment
P = Principal amount (initial investment)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
Now let's calculate it step by step using the given values:
P = $7500 (principal amount)
r = 9% = 0.09 (annual interest rate in decimal form)
n = 12 (compounded monthly, so 12 times per year)
t = 4 (number of years)
Plugging these values into the formula:
A = 7500(1 + 0.09/12)^(12*4)
First, divide the annual interest rate (0.09) by the number of times it's compounded per year (12) to find the monthly interest rate:
Monthly interest rate = 0.09/12 = 0.0075
Now, raise the quantity inside the parentheses to the power of (12*4):
(1 + 0.0075)^(12*4) = (1.0075)^48
Using a calculator, evaluate (1.0075)^48:
(1.0075)^48 ≈ 1.4064
Finally, multiply the principal amount (7500) by the evaluated value:
A ≈ 7500 * 1.4064 ≈ $10,548
Therefore, the total amount of the investment after 4 years, compounded monthly at 9%, is approximately $10,548.