Personal finance who can help?

Question

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 $2500 in a savings account set aside for the furniture. They would like to make 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 8% interest, how much should the year end payments be?

Show all work for each assignment and explain each step carefully

Answer 1

$2500 after 3 years at 8% interest would be worth-
$2500 x (1.08)^3 = 2500 x 1.259712 = $3149.28
If they deposit $X at the end of year 1, 2 years later it would be worth $X times (1.08)^2 or $X times 1.1664
If they deposited $X at the end of year 2, 1 year later it would be worth $X times 1.08. If they deposit $X at the end of year 3, it would be worth $X (at the end of year 3).

$10, 000 = $3,149.28 + (1.08^2 + 1.08 + 1) * $X
$6,850.72 = 3.2464 * $X
$X = 6850.72 / 3.2464 = $2,110.25

Answer 2

Hi,
You can take the labor out of this problem or alternately check your answer if you need to do the details by using the Finance APP of a TI-83 Plus, TI-84 or similar calculator. I’ll cover that after I do it the hard way.
This is like a sinking fund or annuity, with the amount of principal and interest on the present value of $2500 subtracted from the future value.
The amount of the present value after 3 years is this:
A = PV(1+i)^n
= 2500 (1.08)^3
= 3149.28
Subtracting that from the total future value we get 6850.72 for the future value of the sinking fund part.
So, we have this formula:
P = FVi/((1+i)^n-1)
=(6850.72*.08)/((1.08)^3)-1)
Plug that into your calculator and you’ll get 2110.25 for the payment.

Now to do it with a TI-83 Plus for TI-84:
a) Press APPS, ENTER, ENTER to go to the Finance APP.
b) Enter the following: I% = 8; PV = -2500 (Make sure you use the negative sign and not the minus sign.);FV = 10000; P/Y = 1; C/Y = 1; PMT: END.
c) Move the cursor to PMT and press ALPHA, SOLVE (The ENTER button.). The answer, -2110.2513, will be displayed. The minus sign just indicates a payment. That's standard using cash flow methods.

FE

Answer 3

2500
interest on 2500 end of year 1 plus 200.00
Deposit 2110.25
interest on 4810.25 end of year 2 plus 384.82
Deposit 2110.25
interest on 7305.32 end of year 3 plus 584.43
Deposit 2110.25