You deposit $1200 into an account that pays 6% annual interest, compounded continuous. Find the balance of the account after 3 years.

Answer 1

Kyla,

an account that pays 6% annual interest, the principal grows in the following way

you multiply the principal by the factor 1.06 to get the next amount one year later:

now: Amount = Principal of $1200

after t=1year: Amount A_1= principal *(1.06) = 1272 = Principal + Interest (you multiply by the factor 1.06 to get the next amount one year later

New principal:1272

after t=2 years: A_2= 1272*(1.06) = or 1200*(1.06)^2 = 1348.32

New principal is 1348.32

after t=3 years: A_3 = 1348.32*(1.06) = or 1200(1.06)^3=1429.22

Using the coumpound interest formula: A=P(1+r/n)^(nt)

Set n=1 (compound once a year)--->nt = t

r=0.06

1+r = 1.06

Therefore after t=3 years, A =1200(1.06)^3 =1429.22

Answer 2

A = 1200e⁰⁰⁶⁽³⁾

A = 1200e^0.18

A ≈ 1200(1.197)