Question

What is the APY of a savings account with an APR of 3.9886% and compounded quarterly.

Answer 1

APY = 4.0486561%

Explanation:

Given is the Annual Percentage Rate (APR) = 3.9886% compounded quarterly.

Suppose Principal amount, P = $1.

time, t = 1 year.

interest rate, r = 3.9886% = 0.039886

period of compounding, n = 4 (for quarterly).

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

FV = 1 * (1 + 0.039886/4)^(1*4) = 1.040486561

Annual Percentage Growth = (FV/P)*100 = (1.040486561 / 1) * 100 = 4.0486561%

Hence, Annual Percentage Yield (APY) = 4.0486561%

Answer 2

The APY of the saving account is 4.048656%

Explanation:

We know the formula for APY which is given by

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

here, r= interset rate = 3.9886% = 0.039886

n = compounding cycles = 4

On plugging these values in the above formula, we get

`APY=(1+( 0.039886)/(4) )^4-1`

On simplifying this we get

APY = 0.04048656 =4.048656%