Use the compound interest formula for compounding more than once a year to determine the accumulated balance after the stated period.
$1800 deposit at an APR of 5% with quarterly compounding for 4 years
The compound interest formula with quarterly compounding is:
A = P * (1 + r/n)^(n*t)
Where:
A = Accumulated balance
P = Principal amount (initial deposit) = $1800
r = Annual interest rate expressed as a decimal = 5% = 0.05
n = Number of compounding periods per year = 4 (quarterly compounding)
t = Number of years = 4
Plugging in the values:
A = 1800 * (1 + 0.05/4)^(4*4)
A = 1800 * (1 + 0.0125)^(16)
Now we can calculate this using a calculator:
A ≈ $2,078.66
Therefore, the accumulated balance after 4 years with quarterly compounding would be approximately $2,078.66.
To determine the accumulated balance after 4 years with quarterly compounding, we can use the compound interest formula for compounding more than once a year.
The compound interest formula is given by:
A = P(1 + r/n)^(nt)
Where:
A = the accumulated balance after a certain period
P = the principal deposit amount
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case:
P = $1800
r = 5% or 0.05 (as a decimal)
n = 4 (quarterly compounding)
t = 4 years
Substituting these values into the formula:
A = 1800(1 + 0.05/4)^(4*4)
Simplifying:
A = 1800(1 + 0.0125)^(16)
Calculating the value inside the parentheses:
A = 1800(1.0125)^(16)
Using a calculator, we can calculate:
A ≈ $2073.43
Therefore, the accumulated balance after 4 years with quarterly compounding at an APR of 5% will be approximately $2,073.43.
To calculate the accumulated balance using the compound interest formula with quarterly compounding, we need to 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 the interest is compounded per year
t = Number of years
In this case, let's plug in the values given:
P = $1800
r = 5% (or 0.05 in decimal form)
n = 4 (quarterly compounding; 4 times a year)
t = 4 (4 years)
A = 1800(1 + 0.05/4)^(4*4)
First, let's calculate the expression inside the parentheses:
1 + 0.05/4 = 1.0125
Next, let's calculate the exponent:
4 * 4 = 16
Now, let's substitute these values back into the original formula:
A = 1800 * (1.0125)^16
Calculating this expression will give us the accumulated balance after 4 years with quarterly compounding.