Use the compound interest formula to determine the accumulated balance after the stated period. Assume that interest is compounded annually.
$10,000 is invested at an APR of 10% for 5 years.
To determine the accumulated balance after 5 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = accumulated balance after the specified period
P = principal amount (the initial investment)
r = annual interest rate (expressed as a decimal)
n = number of times interest is compounded per year
t = time in years
In this case, the principal amount (P) is $10,000, the annual interest rate (r) is 10% or 0.10, and the time period (t) is 5 years. The question states that interest is compounded annually, so n is equal to 1.
Now we can plug these values into the formula:
A = 10000(1 + 0.1/1)^(1*5)
A = 10000(1 + 0.1)^5
A = 10000(1.1)^5
A = 10000(1.61051)
A ≈ $16,105.10
Therefore, the accumulated balance after 5 years is approximately $16,105.10.
To determine the accumulated balance after 5 years using the compound interest formula, you can use the following formula:
A = P(1 + r/n)^(nt)
Where:
A = Accumulated balance
P = Principal amount (initial investment)
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 amount (P) is $10,000, the annual interest rate (r) is 10% (or 0.10 as a decimal), the number of times interest is compounded per year (n) is 1 (as it is compounded annually), and the number of years (t) is 5.
Using these values, we can calculate the accumulated balance (A):
A = $10,000(1 + 0.10/1)^(1*5)
A = $10,000(1 + 0.10)^5
A = $10,000(1.10)^5
A ≈ $16,105.10
Therefore, the accumulated balance after 5 years will be approximately $16,105.10.
To determine the accumulated balance using the compound interest formula, you can use the following formula:
A = P(1 + r/n)^(nt)
Where:
A = the accumulated balance or total amount
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $10,000, the annual interest rate (r) is 10% (0.10 in decimal form), the number of times interest is compounded per year (n) is 1 (since it is compounded annually), and the number of years (t) is 5.
Substituting these values into the formula:
A = $10,000(1 + 0.10/1)^(1*5)
Calculating the exponent first:
(1 + 0.10/1)^(1*5) = (1 + 0.10)^5 = (1.10)^5 = 1.61051
A = $10,000 * 1.61051
A ≈ $16,105.10
Therefore, the accumulated balance after 5 years would be approximately $16,105.10.