Question

you invest 2000 in an account that is compounded continuously at an interest rate of 5. You never withdrawal money from the account. Which equation gives the amount of money you will have in the account after t years?

Answer 1

The equation that gives the amount of money you will have in the account after t years is: f(t) = 2,000 + 1.05^t

Given:
Principal = 2,000
Interest Rate = 5%

The term compounded continuously means that interests on the principal also earn interest.

Let f(t) be the total amount of money in the account after t years.

f(t) = 2,000 * 1.05^t

1.05 is raised to the power of t. t denotes the number of times 1.05 be multiplied to the principal.

assuming t = 5 years
f(5) = 2,000 * 1.05⁵
       = 2,000 * 1.28         * 1.05 x 1.05 x 1.05 x 1.05 x 1.05 = 1.28
f(5) = 2,553