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 for the 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 end payments be? and please explain.. Thanks for your time

1500(1.06)^3 + paym(1.06^3 - 1)/.06 = 10000

paym(3.1836) = 10000 - 1786.52
payment = 8213.476/3.1836 = 2579.93

To find out how much each year-end payment should be, we need to calculate the future value of the savings account with the initial deposit and the interest earned over the three-year period.

Here's how you can calculate it step by step:

Step 1: Calculate the future value of the initial deposit.
You have mentioned that Mary and Joe currently have $1500 in a savings account. To find out the future value of this deposit after three years, we can use the formula for calculating compound interest:

Future Value = Present Value * (1 + Interest Rate)^Time

Present Value = $1500
Interest Rate = 6% (or 0.06 as a decimal)
Time = 3 years

Future Value = 1500 * (1 + 0.06)^3
Future Value = 1500 * (1.06)^3
Future Value ≈ $1785.36 (rounded to two decimal places)

So, the future value of the initial deposit after three years is approximately $1785.36.

Step 2: Calculate the total future value of the savings account.
Mary and Joe want to have $10,000 in their savings account after three years. Since they already have $1500, they need to calculate how much they need to save in the account over the three-year period to reach the target amount.

Total Future Value = Target Future Value - Initial Deposit
Total Future Value = $10,000 - $1785.36
Total Future Value ≈ $8214.64 (rounded to two decimal places)

So, the total future value of the savings account after three years should be approximately $8214.64.

Step 3: Calculate the equal year-end payments.
Since Mary and Joe want to make three equal year-end deposits, we can divide the total future value of the savings account by 3 to find out how much each payment should be.

Year-end Payment = Total Future Value / Number of Payments
Year-end Payment = $8214.64 / 3
Year-end Payment ≈ $2738.21 (rounded to two decimal places)

Therefore, each year-end payment should be approximately $2738.21 for Mary and Joe to save up $10,000 by the end of three years to buy new furniture for their home.