Question

What is the APY of a savings account with an APR of 3.9742% compounded monthly? Answer to the four decimal place

Answer 1

APY = 4.0474%

Explanation:

Given is the Annual Percentage Rate (APR) = 3.9742% compounded monthly.

Suppose Principal amount, P = $1.

time, t = 1 year.

interest rate, r = 3.9742% = 0.039742

period of compounding, n = 12 (for monthly).

Future value = P * (1 + r/n)^(nt)

FV = 1 * (1 + 0.039742/12)^(1*12) = 1.040473955

Annual Percentage Growth = (FV/P)*100 = (1.040473955 / 1) * 100 = 4.0473955%

Hence, Annual Percentage Yield (APY) = 4.0474%

Answer 2

The APY of the saving account is 4.0474%

Explanation:

We know the formula for APY which is given by

`APY=(1+(r)/(n) )^n-1`

here, r= interset rate = 3.9742% = 0.039742

n = compounding cycles = 12

On plugging these values in the above formula, we get

`APY=(1+(0.039742)/(12) )^(12)-1`

On simplifying this we get

APY =0.04047395=4.0474%