find how much interest $15,000 earns in two years in a certificate paying 4.5% interest compounded quarterly?
interest = 15000(1.01125)^8 - 15000
= ...
1404.37
To calculate the interest earned on a certificate, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A: Total amount after interest
P: 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, P = $15,000, r = 4.5% (or 0.045 as a decimal), n = 4 (quarterly compounding), and t = 2 years.
Plug in the values into the formula:
A = 15000(1 + 0.045/4)^(4*2)
Simplifying the equation:
A = 15000(1.01125)^8
A ≈ 15000(1.09258)
A ≈ $16,388.68
To find the interest earned, subtract the principal amount from the total amount:
Interest = A - P
= $16,388.68 - $15,000
≈ $1,388.68
Therefore, the interest earned on a certificate paying 4.5% interest compounded quarterly for two years on $15,000 is approximately $1,388.68.
To find how much interest $15,000 will earn in two years in a certificate paying 4.5% interest compounded quarterly, follow these steps:
Step 1: Convert the annual interest rate to a quarterly interest rate.
- The annual interest rate is 4.5%.
- Divide the annual interest rate by the number of compounding periods in a year (4 quarters): 4.5% / 4 = 1.125%.
Step 2: Calculate the total number of compounding periods:
- Since the interest is compounded quarterly, the total number of compounding periods is 2 years * 4 quarters = 8 periods.
Step 3: Calculate the future value (including interest) using the compound interest formula:
- Future Value = Principal * (1 + (Interest Rate / 100)) ^ Number of Periods
- Principal = $15,000 (given)
- Interest Rate = 1.125% (quarterly interest rate in decimal form)
- Number of Periods = 8 (total number of compounding periods)
Plugging in the numbers into the formula, we get:
Future Value = $15,000 * (1 + (1.125 / 100))^8
Step 4: Calculate the interest earned by subtracting the principal amount:
- Interest Earned = Future Value - Principal
Now, let's calculate the interest earned:
Future Value = $15,000 * (1 + (1.125 / 100))^8
Future Value = $15,000 * (1 + 0.01125)^8
Future Value = $15,000 * (1.01125)^8
Future Value = $15,000 * 1.093713176
Interest Earned = Future Value - Principal
Interest Earned = ($15,000 * 1.093713176) - $15,000
Using a calculator, we find that the future value is approximately $16,405.70, and the interest earned is approximately $1,405.70.
Therefore, $15,000 will earn approximately $1,405.70 in interest over two years in a certificate paying 4.5% interest compounded quarterly.