Use the compound interest formula for compounding more than once a year to determine the accumulated balance after the stated period.
$3000 deposit at an APR if 6% with monthly compounding for 6 years
The compound interest formula for compounding more than once a year is:
A = P(1 + r/n)^(nt)
Where:
A = the accumulated balance after the stated period
P = the principal (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, the principal (P) is $3000, the annual interest rate (r) is 6% which is equal to 0.06, the number of times interest is compounded per year (n) is 12 (monthly compounding), and the number of years (t) is 6.
We can plug these values into the formula:
A = 3000(1 + 0.06/12)^(12*6)
A = 3000(1 + 0.005)^72
A = 3000(1.005)^72
A = 3000(1.432364654)
A ≈ $4,297.09
Therefore, the accumulated balance after 6 years with monthly compounding is approximately $4,297.09.
To determine the accumulated balance after 6 years with monthly compounding, we can use the compound interest formula for compounding more than once a year:
A = P(1 + r/n)^(nt)
Where:
A = Accumulated balance
P = Principal amount (initial deposit)
r = Annual interest rate (in decimal form)
n = Number of times the interest is compounded per year
t = Number of years
Given:
P = $3000
r = 6% or 0.06
n = 12 (monthly compounding)
t = 6 years
Now, let's substitute these values into the formula and calculate the accumulated balance:
A = 3000(1 + 0.06/12)^(12*6)
Simplifying the formula:
A = 3000(1 + 0.005)^(72)
A = 3000(1.005)^(72)
Using a calculator, we can find:
A ≈ 3000 * 1.400250032730875
A ≈ $4,200.75
Therefore, the accumulated balance after 6 years with monthly compounding will be approximately $4,200.75.
To determine the accumulated balance using the compound interest formula with compounding more than once a year, we can use the following formula:
A = P(1 + r/n)^(nt)
Where:
A = Accumulated balance
P = Principal amount (initial deposit)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
In this case, we have a $3000 deposit at an APR (Annual Percentage Rate) of 6% with monthly compounding over a period of 6 years.
First, let's convert the annual interest rate to decimal form:
r = 6% = 0.06
Next, let's substitute the given values into the formula:
P = $3000
r = 0.06
n = 12 (since interest is compounded monthly)
t = 6
Now, we can calculate the accumulated balance:
A = 3000(1 + 0.06/12)^(12*6)
A = 3000(1 + 0.005)^72
A = 3000(1.005)^72
A ≈ $4089.46
Therefore, the accumulated balance after 6 years with monthly compounding is approximately $4089.46.