[I wrote this post a few months ago in a Saverocity forum in reference to the 6% Savings account attached to the Mango prepaid card as an explanation of how to compute your effective yield/expected interest on the account.]

Here’s the formula for continuous compounding of interest:

A_t = P * e ^ rt

A_t = amount after time t (in years)
P = principal
e = a constant
r = rate
t = time (in years)

We’re told APY is 6%. Therefore:

A = 1.06 * P

Divide by P since we’re only considered about the rate (since A will scale linearly with an increase in P) and we get:

1.06 = e ^ rt
ln(1.06) = rt

Since t = 1, we have:

r = ln(1.06) = 0.0582

Therefore APR ~ 5.82%

Factoring in the monthly fee, you have:

r_actual ~ 0.0582 - 36/5000 = 0.051

Therefore APR_actual ~ 5.1%

The reason we care about APR and not APY is because of the $5000 cap. The interest you earn won’t actually earn full interest, so you can’t realize the 6% value they cite.


[Note that we actually have daily compounding instead of continuous, so the rate is a touch higher, which is how we get $24.84 – $3 = $21.84 per month. However, as many people have mentioned, you do pay taxes on the interest earned before subtracting out the fee, which is kind of crappy, but it’s only about $10 even for higher tax brackets]