Question

Carla Lopez deposits $1,500 a year into her retirement account. If these funds have an average earnings of 7 percent over the 40 years until her retirement, what will be the value of her retirement account at the time

Answer 1

To calculate the future value of Carla Lopez's retirement account with $1,500 annual deposits and a 7% return rate over 40 years, the formula for the future value of an annuity is used, resulting in an approximate value of $305,700 upon retirement.

Step-by-step explanation:

Calculating Retirement Account Value

The question asks for the future value of a retirement account when $1,500 is deposited annually at an average earnings rate of 7% over 40 years. To solve this, we use the formula for the future value of an annuity: FV = P × [(1 + r)^nt - 1] / r, where P is the annual payment, r is the interest rate per period, t is the number of periods per year, and n is the number of years.

Substituting our given values, we get FV = $1,500 × [(1 + 0.07)^1×40 - 1] / 0.07. Calculating this gives us the future value of Carla's retirement account.

As an example, let's say Carla deposits the $1,500 at the end of each year. After 40 years of depositing $1,500 at 7%, compounded annually, Carla's retirement account will grow to approximately $305,700.