A young couple wants to start a family in five years time. They plan to add an addition to their home in four years so it is ready when they start their family. They estimate that $90,000 will be needed in four years. They can earn 5% on an investment now. If the couple adds money to an investment at a continuous, constant rate for the entire four-year period, at what rate (in dollars per year) should the money be deposited in order to reach the goal of $90,000 in four years?

Question

Quizplus · Accepted Answer

The amount of money that needs to be deposited at a continuous, constant rate for four years in order to reach the goal of $90,000 can be calculated using the formula:```P = A * (1 - e^(-rt)) / r```where:* P is the amount of money that needs to be deposited* A is the goal amount* r is the annual interest rate* t is the number of yearsIn this case, A = $90,000, r = 5%, and t = 4. Plugging these values into the formula, we get:```P = 90000 * (1 - e^(-0.05*4)) / 0.05``````P = 90000 * (1 - e^(-0.2)) / 0.05``````P = 90000 * (1 - 0.8187) / 0.05``````P = 90000 * 0.1813 / 0.05``````P = 20,325```Therefore, the couple should deposit $20,325 per year in order to reach their goal of $90,000 in four years.

A Young Couple Wants to Start a Family in Five