How much more would $1,000 earn in 5 years in an account compounded continuously than an account compounded quarterly if the interest rate on both accounts is $3.7%

There is a difference of $ 1.0228.

Explanation: Given, initial amount or principal = $ 1000,

Time= 5 years and given compound rate of interest = $3.7%

Now, Since the amount in compound continuously,

, where, r is the rate of compound interest, P is the principal amount and t is the time.

Here, P=$ 1000, t=5 years and r= $3.7%,

Thus, amount in compound continuously ,  

⇒

Therefore, interest in this compound continuously rate =1203.21844013-1000=203.21844013

now, Since the amount in compound quarterly,

, where, r is the rate of compound interest, P is the principal amount and t is the time.

Thus, amount in compound quarterly,

⇒

⇒

⇒

Therefore, interest in this compound quarterly rate=1202.19567617-1000=202.19567617

So, the difference in these interests=203.21844013-202.19567617=1.02276396 ≈1.0228                                                  

goog may have it for you