Question

Beatriz deposited money into a savings account that earns interest 20 years ago, and she has not deposited or withdrawn money from the account since then. The following information provides the value of the account at various times. 10 years ago, the account had a balance of 1629 , 5 years ago, the account had a balance of 2079 , Today, the account has a balance of 2653 Create an equation that can be used to model the balance of the account, a , after t years since the initial deposit into the account. Then, use the equation to determine the balance of the account after 20 more years. The equation that represents this scenario is: The balance of the account after 20 more years will be Response area

Answer 1

a = 1629(1 + r)^t

Where:
a = balance of the account after t years
r = annual interest rate
t = number of years since the initial deposit

Using the information given, we can solve for the annual interest rate:

2079 = 1629(1 + r)^5
1.274 = (1 + r)^5
Taking the fifth root of both sides:
1.081 = 1 + r
r = 0.081 or 8.1%

Now that we have the annual interest rate, we can determine the balance of the account after 20 more years:

a = 1629(1 + 0.081)^20
a = 1629(1.081)^20
a ≈ 6556.78

Therefore, the balance of the account after 20 more years will be approximately 6556.78.