A deposit of 3500 is made in an account that earns 8 interes

A deposit of $3500 is made in an account that earns 8% interest compounded quarterly. The balance in the account after n quarters is given by the following sequence. Find the balance in the account after two years.

a_n=3500(1+ 0.08/4)ⁿ , n = 1,2,3

the balance after two years is $ [ ] . (Do not round unit the final answer. then round to the nearest cent as needed.)

Solution

Formula for compound interest compounded quartely :

Amount = Principal[ 1+rate/4]^(4*t)

Balance after two years ; t=2

= 3500[ 1+0.08/4]^(2*4)

= 3500[ 1.02]^8

= 4100.8078

= $4100.81