Question

An initial deposit of $35,000 grows at an annual rate of 7% for 23 years. Compare the final balances resulting from continuous compounding and annual compounding. We're supposed to use the equation A=P(1+r/k)^kt but I don't know what I'm supposed to use for k when the compounding is continuous. Thanks.

Answer 1

There is a special formula for continuous compounding
it is
Amount = Principal (e^(rt) ) where r is the annual rate compounded continuously and t is the number of years.

So for annual compounding
amount = 35000(1.07)^23 = 165 918.55

continuous compounding
amount = 35000(e^(23(.07)) = 175 098.39

Answer 2

thanks so much!