How much would 100 invested at 4 percent interest compounded continuously be worth after 7 years?

Answer 1

The formula for the amount received (A) when investing P after n periods where the rate per period is r% is given by:

A = P(1+ r/100)n

If you have an apr (annual percentage rate) and it is applied monthly, then the rate is apr ÷ 12 applied 12n times (for n years).

So going back to your question:

I assume the 4% is 4% apr.

So the return if the interest is applied yearly would be:

A = 100 x (1 + 0.04)7

~= 131.59

However, you specify continuously - what exactly does "continuously" mean. Let suppose that the interest is applied monthly, then:

A = 100 x (1 + 0.04/12)7 x 12

~= 132.25

Hmmm...we got a little more; how about more often, say daily (I'll ignore the fact of leap years and assume 365 days per year):

A = 100x (1 + 0.04/365)7 x 365

~= 132.31

Not much more, how about hourly (still assuming 365 days/year):

A = 100x (1 + 0.04/8760)7 x 8760

~= 132.31

(There's actually a difference, but not big enough to show in monetary terms). Going to every minute:

A = 100x (1 + 0.04/525600)7 x 525600

~= 132.31

We seem to have hit a limit!

The actual return you will get if the (100r)% apr was applied continuously for n years is:

A = Pern

So for 100 at 4% apr for 7 years, this is:

A = 100e0.04 x 7

~= £132.31