Question

You invest $2,000 in an account that is compounded annually at an interest rate of 5%. You never withdraw money fro

the account. Which equation below gives the amount of money you will have in the account after tyears?
Al = 2,000 20.05
Al = 2,000(1.5)
A10 = 2,000(105)
A1 = 2.000 e5

Answer 1

`A(t) = 2,000(1.05)^(t)`

Explanation:

The compound interest formula is given by:

`A(t) = P(1 + (r)/(n))^(nt)`

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

You invest $2,000

This means that
`P = 2,000`

Compounded anually

Once a year, so
`n = 1`

Interest rate of 5%.

This means that
`r = 0.05`

Amount after t years:

`A(t) = P(1 + (r)/(n))^(nt)`

`A(t) = 2,000(1 + (0.05)/(1))^(t)`

`A(t) = 2,000(1.05)^(t)`