$3000 is deposited into an account that pays 5% annual interest

Question

$3000 is deposited into an account that pays 5% annual interest for 10 years. How much more would be in the account if the interest were compounded continuously rather than quarterly?

Answer 1

Hi Traci.

 

Amazingly, not all that much. "Compounding continuously" is really more of a marketing ploy than anything else.

 

"That investment firm over there compounds every day but we compound multiple times every SECOND so you NEED to invest with us to get the most out of your money!!"

 

The math doesn't necessarily say so though.

 

If the interest is compounded quarterly use the following formula:

 

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

 

P = principal invested

r = rate of return (5% = 0.05)

n = number of times compounded per year (quarterly = 4)

t = time in years (10)

 

A = 3000*(1 + 0.05/4)^(4*10)

 

= $4,930.86

 

If it's compounded continuously use this formula:

 

A = Pe^(rt)

 

P = principal invested

e = natural number

r = rate of return (0.05)

t = time in years (10)

 

A = 3000*e^(0.05*10)

 

= $4,946.16

 

So the difference is

 

$4,946.16 - $4,930.86 = $15.30

 

$1.53 every year over the course of ten years won't seem like much (it's a little less than half a penny per day), but hey money is money. I just wouldn't be sold by continuously compounded interest over any other compounding rate if the investment firm offering the continuous interest is shady.

 

Hope this helps.