Question

Some banks advertise that money in their accounts is compounded continuously. To get an understanding of what this​ means, divide the year into 100 comma 000 compounding periods per year. Apply the compound interest formula for finding future value to approximate what the effective yield would be if the compounding were done continuously for the stated nominal yield.

nominal​ yield, 19​%

Answer 1

20.9249%

Explanation:

The effective yield for rate r compounded n times per year is ...

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

For r=0.19 and n=100,000, the yield is ...

APY = (1 +0.0000019)^100000 -1 ≈ 0.209249379 ≈ 20.9249%

_____

The actual yield for continuous compounding is ...

APY = e^r -1

For r=0.19, this is APY ≈ 0.209249598

This value differs from the above in the 7th decimal place. Rounding to 6 decimal places would give different values.