Question

find the amount in an account after years if invested$5000 at 6% per year and is compounded quarterly​

Answer 1

The amount of money in the account after t years is given by:
`A(t) = 5000(1.015)^(4t)`

Explanation:

Compound interest:

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.

Invested $5000 at 6% per year and is compounded quarterly​

This means, respectively, that
`P = 5000, r = 0.06, n = 4`

So, the amount of money in the account after t years will be given by:

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

`A(t) = 5000(1 + (0.06)/(4))^(4t)`

`A(t) = 5000(1.015)^(4t)`