Question

1. Eloise is investing in a retirement account. She plans on adding an additional $50 at the end of every year and the expected monthly rate of return is 4% of the amount invested, calculated at the end of the month. If she starts with $1000 in the account find an equation that models the amount of money in the account each month for the first year.

Answer 1

To model the amount of money in Eloise's retirement account each month for the first year, we can use the formula for compound interest. Using the given values, the amount in Eloise's account after the first year is approximately $1471.94.

Step-by-step explanation:

To model the amount of money in Eloise's retirement account each month for the first year, we can use the formula for compound interest. The formula is A = P(1 + r/n)^(nt), where A is the amount of money accumulated, P is the principal amount (initial investment), r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.

In this case, Eloise starts with $1000 in the account, so P = 1000. The expected monthly rate of return is 4%, which translates to an annual interest rate of 4% * 12 = 48%. Thus, r = 48%. Since the interest is calculated at the end of each month, n = 12. Finally, we want to model the amount for the first year, so t = 1.

Plugging in the values into the formula, we get A = 1000(1 + 0.48/12)^(12*1). Simplifying the expression, A = 1000(1.04)^12. Calculating this expression, A ≈ $1471.94.