Question

111. Dani has $1,000 in an investment account that earns 3% per year, compounded monthly.

c. Write an explicit formula for the amount of money in her account after t years.

Answer 1

`A(t) = 1000(1.0025)^(12t)`

Explanation:

The compound interest formula is given by:

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

Where A(t) is the amount of money in the account 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 unit t and t is the number of years the money is invested or borrowed for.

For this problem, we have that:

`P = 1000`

The investment is compounded monthly. There are 12 months in a year. So
`n = 12`

The interest rate is 3%. So
`r = 0.03`.

So

The amount of money in her account after t years is:

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

`A(t) = 1000(1 + (0.03)/(12))^(12t)`

`A(t) = 1000(1.0025)^(12t)`