Question

Five thousand dollars is deposited into a savings account at 2.5% interest compounded continuousiy

(a) What is the formula for A(t), the balance after tyears?
(b) What difterential equation is satisfied by A(D), the balance after t years?
(c) How much money wil be in the account afer 8 years?
(d) When will the balance reach 57000 ?
(e) How fast is the balance growing when it reaches $7000 ?

Answer 1

This calculation involves continuous compound interest. The $(A)t$ is calculated using the formula $A(t) = Pe^{rt}$. The differential equation representing this situation is dA/dt = rA(t), and by plugging in various values into the equations, you can know the balance in the account after certain years, when it will reach a specific amount, and how fast it's growing at a certain point.

Step-by-step explanation:

The question is about understanding the principle of continuous compounding in finance, here, with an initial deposit of five thousand dollars at an annual interest rate of 2.5% compounded continuously.