Question

$3000 is deposited in an account

that pays 5% interest,
compounded quarterly, for 10
years. How much more would be
in the account if the interest were
compounded continuously rather
than quarterly?

Answer 1

$15.30

Explanation:

The formula for the account balance with continuous compounding is ...

A = Pe^(rt)

For the given values, this is ...

A = $3000·e^(0.05·10)

A ≈ $4946.16 . . . . balance with continuous compounding

__

The amount with quarterly compounding is ...

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

A = $3000(1 +.05/4)^(4·10)

A ≈ $4930.86 . . . . balance with quarterly compounding

__

The difference is ...

$4946.16 -4930.86 = $15.30

The continuously compounded account would earn $15.30 more in 10 years.