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 for compounding more than once a year is:
A = P(1 + r/n)^(nt)
Where:
A = Accumulated balance
P = 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:
P = $1800
r = 5% = 0.05
n = 4 (quarterly compounding)
t = 4 years
Plugging the values into the formula:
A = 1800(1 + 0.05/4)^(4*4)
A = 1800(1 + 0.0125)^16
A = 1800(1.0125)^16
Calculating the value inside the brackets:
(1.0125)^16 ≈ 1.217
Multiplying:
A ≈ 1800 * 1.217
A ≈ $2190.60
Therefore, the accumulated balance after 4 years with quarterly compounding is approximately $2190.60.
To calculate the accumulated balance using the compound interest formula for compounding more than once a year, we need to use the formula:
A = P(1 + r/n)^(nt)
Where:
A = Accumulated balance
P = Principal amount (initial deposit)
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
Given:
P = $1800
r = 5% = 0.05 (as a decimal)
n = 4 (quarterly compounding)
t = 4 years
Plugging in the values into the formula, we get:
A = 1800(1 + 0.05/4)^(4*4)
Calculating the brackets first:
A = 1800(1 + 0.0125)^(16)
Next, we calculate the exponent:
A = 1800(1.0125)^(16)
Finally, we calculate the accumulated balance:
A ≈ $2200.77
Therefore, the accumulated balance after 4 years with a $1800 deposit at an APR of 5% with quarterly compounding is approximately $2200.77.
To determine the accumulated balance after the stated period using the compound interest formula for compounding more than once a year, follow these steps:
Step 1: Convert the Annual Percentage Rate (APR) to a decimal by dividing it by 100. In this case, the APR is 5%, so it becomes 0.05.
Step 2: Divide the APR by the number of compounding periods within a year. In this case, the compounding is done quarterly, so there are 4 compounding periods in a year. Therefore, divide 0.05 by 4, which gives you 0.0125.
Step 3: Add 1 to the result from Step 2. It becomes 1.0125.
Step 4: Raise the result from Step 3 to the power of the total number of compounding periods over the given period. In this case, the deposit is compounded quarterly for 4 years, which leads to a total of 16 compounding periods (4 years x 4 quarters/year = 16). So, calculate 1.0125^16, which gives you 1.2219.
Step 5: Multiply the result from Step 4 by the initial deposit amount. In this case, the initial deposit amount is $1800. So, multiply $1800 by 1.2219, which gives you $2,199.42.
Therefore, the accumulated balance after 4 years with a $1800 deposit at an APR of 5% with quarterly compounding is approximately $2,199.42.