Question

Skylar plans to use $3400 to open a savings account with an annual interest rate of 1.15%. How much more interest will he earn over 13 years if he chooses a compound interest account that compounds interest quarterly instead annually? Round your answer to the nearest cent.

interest compounded annually: A = P (1 + r)t
interest compounded quarterly: A = P (1 +fraction numerator r over denominator 4 end fraction)4t

$

Answer 1

Substitute the given values into the given equations, then evaluate the difference between the results.

Compounded annually, Skylar's balance after 13 years is
A = 3400(1 +.0115)^13 = 3944.90

Compounded quarterly, Skylar's balance after 13 years is
A = 3400(1 + .0115/4)^52 ≈ 3947.42

Using the account where interest is compounded quarterly, Skylar earns additional interest of
$3947.42 - 3944.90 = $2.52