Find the amount A in the account earning compound interest after six years when the principle is $3500. r=2.16%, compounded quarterly.
3500(1 + 0.0216/4)^(4*6) = _____
Well, well, well, looks like we have a math question on our hands. Don't worry, I won't let you down!
To find the amount A in the account after six years, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A is the amount after t years,
P is the principal (initial amount),
r is the annual interest rate (in decimal form),
n is the number of times the interest is compounded per year,
and t is the number of years.
In this case, the principal P is $3500, the annual interest rate r is 2.16% (or 0.0216 as a decimal), and the interest is compounded quarterly, so n is 4. We want to find the amount after 6 years, so t is 6.
Plugging in the values, we get:
A = 3500(1 + 0.0216/4)^(4*6)
Now, let me put on my mathematician's hat and do the calculations for you...
Drumroll, please!
After rigorous calculations, the amount A in the account after six years is approximately $4,149.63.
Voilà! Your money has grown like magic!
To find the amount A in the account earning compound interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial amount)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
Given:
Principal (P) = $3500
Annual interest rate (r) = 2.16% = 0.0216
Number of times interest is compounded per year (n) = quarterly = 4
Number of years (t) = 6
Plugging in these values into the formula, we have:
A = 3500(1 + 0.0216/4)^(4*6)
Now, let's calculate it step-by-step:
Step 1: Calculate the interest rate per compounding period (i) by dividing the annual interest rate (r) by the number of times interest is compounded per year (n):
i = r/n = 0.0216/4 = 0.0054
Step 2: Calculate the exponent by multiplying the number of times interest is compounded per year (n) by the number of years (t):
exponent (nt) = 4 * 6 = 24
Step 3: Calculate the inside of the parentheses:
(1 + i) = (1 + 0.0054)
Step 4: Raise the inside of the parentheses to the power of the exponent:
(1 + i)^(nt) = (1 + 0.0054)^24
Step 5: Calculate the final amount A by multiplying the principal (P) by the result from step 4:
A = 3500 * (1 + 0.0054)^24
Now, we can calculate the final amount A using a calculator.
To find the amount A in the account earning compound interest after six years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount including interest
P = the principal amount (initial investment)
r = annual interest rate (expressed as a decimal)
n = number of times interest is compounded in a year
t = number of years
In this case, the principal amount (P) is $3500, the annual interest rate (r) is 2.16% (or 0.0216 as a decimal), the interest is compounded quarterly, so n equals 4 (quarterly), and the time (t) is 6 years.
Therefore, we can substitute these values into the formula:
A = 3500(1 + 0.0216/4)^(4*6)
Now, let's calculate the expression inside the parentheses first:
1 + 0.0216/4 = 1.0054
Next, let's calculate the exponent:
4 * 6 = 24
Finally, let's substitute these values back into the formula and calculate A:
A = 3500(1.0054)^24
Using a calculator, we can evaluate this expression:
A ≈ 3500 * 1.1487
A ≈ 4024.45
Therefore, the amount A in the account earning compound interest after six years is approximately $4024.45.