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QuestionFind the APY for an account with a 5%5\% interest rate compounded monthly. Options: 5.12%5.12\%, 5.08%5.08\%, 5.21%5.21\%, 5%5\%.

Studdy Solution

STEP 1

Assumptions1. The annual nominal interest rate is5% . The interest is compounded monthly3. We need to calculate the Annual Percentage Yield (APY)

STEP 2

The formula to calculate APY isAPY=(1+rn)nt−1APY = (1 + \frac{r}{n})^{nt} -1where- rr is the annual nominal interest rate (in decimal form) - nn is the number of times the interest is compounded per year- tt is the number of years, which is1 in this case as we are calculating annual yield

STEP 3

First, convert the interest rate from percentage to decimal.
5%=0.055\% =0.05

STEP 4

Now, plug in the values into the APY formula. Here, r=0.05r =0.05, n=12n =12 (as the interest is compounded monthly), and t=1t =1.
APY=(1+0.0512)12×1−1APY = (1 + \frac{0.05}{12})^{12 \times1} -1

STEP 5

Calculate the value inside the parentheses.
APY=(1+0.0512)12−1APY = (1 + \frac{0.05}{12})^{12} -1

STEP 6

Calculate the exponent.
APY=1.0041612−1APY =1.00416^{12} -1

STEP 7

Subtract1 from the result to get the APY in decimal form.
APY=1.0512−1APY =1.0512 -1

STEP 8

Convert the APY from decimal to percentage.
APY=0.0512×100=5.12%APY =0.0512 \times100 =5.12\%The APY for an account that pays5% compounded monthly is5.12%.

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