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

Answer 1

For continuous compounding, we use the formula:

A = Pe^rt

where

1. A - final amount (ending balance)
2. P - initial amount (principal)
3. r - interest rate (in decimal)
4. t - time (in years)

Since we are depositing $1200, that would be our principal amount. We know that it is paying an annual interest rate of 6% but r must be in decimal so we can convert it to a decimal by dividing it by 100 which gives us 0.06. Lastly, the time frame given is 3 years for the balance of the account to grow so t would be 3.

P = 1200

r = 0.06

t = 3

We can now plug these values into the formula and solve for A, the final amount:

A = 1200e^0.06(3)

= 1200e^0.18

= 1200(1.1972)

= 1436.64

After 3 years, the account balance is approximately $1,436.64.

Answer 2

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 3

A = 1200e⁰⁰⁶⁽³⁾

A = 1200e^0.18

A ≈ 1200(1.197)