Find how much interest $15,000 earns in 4 years in a certificate of deposit paying 8.5% interest compounded quarterly.
15,000*[1 + (.085/4)]^16 -15,000
= 20,999.28 - 15,000 = $5999.28
Without compounding, it would be
15,000*.085*4 = $5100.00
This is how much is EARNED and does not include the original $15,000
Oh, interest rates and compounding... they're like old dentures and a merry-go-round, always spinning! Alright, let me calculate this for you.
So, we have $15,000 prancing around in a certificate of deposit at a rate of 8.5% per year. Since it's compounded quarterly, we need to divide that spunky interest rate by 4 to get the quarterly rate. That would be 2.125%.
Now, let's work our magic for each quarter. We'll take the initial amount of $15,000, multiply it by (1 + 0.02125) to account for the quarterly interest, and repeat this for four years because time flies when you're earning interest, my friend.
Ready? After all the calculations, your gleeful little $15,000 will earn about $3,341.23 in interest over four years! Remember, that's just interest, not the whole enchilada. So don't spend it all on balloon animals, unless those are your greatest passion in life!
To calculate the interest earned on a certificate of deposit (CD) with quarterly compounding, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the future value of the investment (including both the principal and interest),
P is the principal amount (initial investment),
r is the annual interest rate (in decimal form),
n is the number of times interest is compounded per year,
t is the number of years.
In this case, the principal amount (P) is $15,000, the annual interest rate (r) is 8.5% or 0.085, interest is compounded quarterly (n = 4), and the time period (t) is 4 years.
Substituting these values into the formula, we have:
A = 15000(1 + 0.085/4)^(4*4)
Calculating this expression will give us the final value of the investment (A), which includes the interest earned.
Let's now perform the calculation step-by-step:
Step 1: Calculate the value inside the parenthesis:
0.085/4 = 0.02125
Step 2: Calculate the exponential part:
4*4 = 16
Step 3: Calculate the value inside the parenthesis + 1:
0.02125 + 1 = 1.02125
Step 4: Raise the value inside the parenthesis + 1 to the power of 16:
1.02125^16 ≈ 1.4015
Step 5: Multiply the principal amount by the result from step 4:
15000 * 1.4015 ≈ $21,022.50
Therefore, the interest earned on a $15,000 CD with an 8.5% interest rate compounded quarterly over 4 years is approximately $6,022.50.
To calculate the interest earned on a certificate of deposit with compound interest, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money accumulated after compounded interest
P = the principal amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $15,000, the annual interest rate (r) is 8.5% (or 0.085 as a decimal), interest is compounded quarterly (n = 4), and the term is 4 years (t = 4).
Plugging these values into the formula:
A = 15000(1 + 0.085/4)^(4*4)
Now we can calculate the interest earned:
A = 15000(1 + 0.02125)^(16)
A = 15000(1.02125)^(16)
A = 15000(1.402551)
A ≈ $21,038.27
Therefore, the interest earned on a $15,000 deposit in a certificate of deposit with an interest rate of 8.5% compounded quarterly, over a 4-year period, is approximately $6,038.27.