A bank advertises a savings account that earns 3% APR compounded daily.
What is the "n" become for the compound interest formula?
What is the APY rate for this loan? Round answer to nearest 100th
there are 365 compounding periods per year
[1 + (.03 / 365)]^365 = 1 + APY
So is this the formula or the answer?
P = Po(1+r)^n.
r = 0.03/365 = 8.22*10^-5/day = Daily % rate.
n = 365 Compounding/yr.
Let Po = $1.00 for this calculation.
P = 1(1.00008.22)^365 = 1.03045.
APY = 1.03045 - 1 = 0.03045 = 3.05%.
okay so when i put P= 1(1.00008.22)^365 in calculator it comes up as an error
the built in Windows calculator (in scientific mode) works pretty well
To determine the value of "n" in the compound interest formula, we need to know how frequently the interest is compounded. In the case of this savings account, it is compounded daily. Therefore, "n" represents the number of compounding periods per year.
Since the interest is compounded daily, we can find "n" by knowing that there are 365 days in a year. Hence, "n" would be equal to 365.
Now, let's calculate the Annual Percentage Yield (APY) rate for this savings account. The APY represents the total amount of interest earned in one year, taking into account the compounding effect.
To calculate the APY rate, we can use the following formula:
APY = (1 + interest rate/n)^n - 1
In this case, the interest rate is 3% APR (Annual Percentage Rate), but we need to convert it to a decimal. So, 3% becomes 0.03.
Substituting the values into the formula:
APY = (1 + 0.03/365)^365 - 1
Calculating this expression will give us the APY rate for the savings account. Rounding it to the nearest hundredth:
APY ≈ 0.030416 or 3.04%
Therefore, the APY rate for this savings account is approximately 3.04%.