Question

A student starts a saving account with a deposit of $500. The account pays 5% interest compounded quarterly. if the student adds no additional money to the account and takes no money out of the account, how much will the account be after three years?

Answer 1

The account balance after three years is approximately $580.38

Explanation:

The given parameters are;

The principal amount deposited,
`P_0` = $500

The interest rate on the account, r = 5% = 0.05

The rate of interest, k = Quarterly = 4

The time of the investment N = 3 years

The formula for the account balance,
`P_N`, after a given N time period is given as follows;

`P_N = P_0 * \left (1 + (r)/(k) \right )^(n * k)`

Substituting the values, gives;

`P_3 =500 * \left (1 + (0.05)/(4) \right )^(3 * 4) = 580.38`

The account balance after three years ≈ $580.38.