calculate the compound interest on an investment of $18,000 at 8% interest compounded quarterly for 15 months.
To calculate compound interest, we will 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 (in decimal form)
n = number of times the interest is compounded per year
t = number of years
In this case, the principal amount (P) is $18,000, the annual interest rate (r) is 8% or 0.08, the interest is compounded quarterly (n = 4 times per year), and the time period (t) is 15 months or 15/12 = 1.25 years.
Now, let's calculate the compound interest step-by-step:
Step 1: Convert the annual interest rate to quarterly interest rate:
Quarterly interest rate (r/n) = 0.08/4 = 0.02 (2%)
Step 2: Calculate the exponent term:
Exponent term (nt) = 4 * 1.25 = 5
Step 3: Apply the formula to calculate the final amount (A):
A = $18,000 * (1 + 0.02)^(5)
Using a calculator:
A = $18,000 * (1.02)^5
A ≈ $21,196.89
So, the compound interest on the investment of $18,000 at 8% interest compounded quarterly for 15 months is approximately $21,196.89 - $18,000 = $3,196.89.
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 ($18,000)
r = the annual interest rate (8% or 0.08)
n = the number of times interest is compounded per year (quarterly, so 4 times)
t = the time the money is invested (15 months or 1.25 years)
First, let's convert the interest rate to a quarterly rate:
Quarterly interest rate = (1 + annual interest rate)^(1/n) - 1
Quarterly interest rate = (1 + 0.08)^(1/4) - 1
Quarterly interest rate ≈ 0.0198 or 1.98%
Now, we can use the formula to find the future value (A):
A = 18,000(1 + 0.0198)^(4 * 1.25)
A ≈ 18,000(1.0198)^5
A ≈ 18,000(1.10464)
A ≈ 19,882.32
The future value (A) of the investment is approximately $19,882.32.
To calculate the compound interest, we subtract the principal amount (P) from the future value (A):
Compound interest = A - P
Compound interest = 19,882.32 - 18,000
Compound interest ≈ $1,882.32
Therefore, the compound interest on an investment of $18,000, at 8% interest compounded quarterly for 15 months, is approximately $1,882.32.