Refer to Narrative 11-1. Calculate The compound interest on an investment of $7,500 at 8% intrest, compounded quarterly, for 8 years
To calculate the compound interest on an investment, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
Given:
P = $7,500
r = 8% = 0.08 (as a decimal)
n = 4 (compounded quarterly)
t = 8 years
Plugging the values into the formula, we have:
A = $7,500(1 + 0.08/4)^(4 * 8)
First, let's simplify the expression inside the brackets:
1 + 0.08/4 = 1 + 0.02 = 1.02
A = $7,500(1.02)^(32)
Now, let's calculate the exponent:
(1.02)^(32) ≈ 1.848932422
Finally, multiply the principal amount by the result:
A = $7,500 * 1.848932422
A ≈ $13,867.99
The compound interest on an investment of $7,500 at 8% interest, compounded quarterly, for 8 years is approximately $13,867.99.
To calculate the compound interest on an investment, you can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, your investment of $7,500 is subject to an 8% interest rate compounded quarterly for 8 years.
Plugging the values into the formula:
P = $7,500
r = 8% = 0.08 (as a decimal)
n = 4 (quarterly compounding)
t = 8
A = 7500(1 + 0.08/4)^(4*8)
Now let's solve it step by step:
Step 1: Calculate the factor inside the parentheses:
1 + 0.08/4 = 1.02
Step 2: Calculate the exponent:
4 * 8 = 32
Step 3: Raise the factor to the power of the exponent:
(1.02)^32 ≈ 1.029563
Step 4: Multiply the result by the principal amount:
A = 7500 * 1.029563 ≈ $9,721.22
Therefore, the future value (including compound interest) on the investment of $7,500 at an 8% interest rate, compounded quarterly for 8 years, is approximately $9,721.22.