Mary and Joe would like to save up $10,000 by the end of three years from now to buy new furniture for their home. They currently have $1500 in a savings account set aside forthe furniture. They would like to make three equal year end deposits to this savings account to pay for the furniture when they purchase it three years from now. Assuming that this account pays 6% interest, how much should the year and payments be?

To calculate the amount of equal year-end payments needed to save up $10,000 in three years, we need to consider the interest earned on the initial savings and the additional deposits.

The compound interest formula can be used to calculate the future value of an investment:

FV = PV * (1 + r)^n

Where:
FV is the future value (in this case, $10,000)
PV is the present value (in this case, $1500)
r is the interest rate (6% or 0.06)
n is the number of years (3)

Plugging in the values, we get:

$10,000 = $1500 * (1 + 0.06)^3

Simplifying the equation:

$10,000 = $1500 * (1.06)^3

$10,000 = $1500 * 1.191016

Now, we need to find the equal year-end payment required. Let's assume the payment amount is P.

We can express the future value of each year-end payment as:

$10,000 = P * (1 + 0.06)^2 + P * (1 + 0.06)^1 + P

Simplifying:

$10,000 = P * 1.1236 + P * 1.06 + P

$10,000 = 3.1836P

Dividing both sides by 3.1836:

$10,000 / 3.1836 = P

P ≈ $3,141.85

Therefore, Mary and Joe should make approximately $3,141.85 year-end payments to save up $10,000 for their furniture purchase in three years.