# Math Help - [SOLVED] Simple Annuities

1. ## [SOLVED] Simple Annuities

I want to know if i have the right thing on these questions i have here.

Mrs. Yang signed a contract with a local furniture company for the purchase of furniture for her new office. The contract requires her to make a downpayment of $3,000.00 and for a monthly payment of$315 per month for the next 3 years. Given that she is charged interest at the rate of $\mbox J_{12} =8$%.

a) How much does the furniture cost?

b) Mrs. Yang missed the first 10 payments. Just before her 11th payment is due, she wins the lotto. What must her payment be to pay off the entire debt?

I am getting the answer for a) to be $13,052.22; and b) would be$3582.84 + a balance of $6,469.38 to make a total of$10,052.22.

HOw wrong am i??

2. Can you show your work? How did you obtained a) and b)...

3. x= 3000+ $315 * \left[ \frac{1-(1.0067)^{-36}}{0.0067} \right]$
= 3000+10,052.22
= 13,052.22

$315 * \left[ \frac{(1.0067)^{11}-1}{0.0067} \right]$=3582.84
Payment = 3582.84 + (315*24)(1.08^(-24))
= 3582.84 + 1192.21
= 4775.05

(the previous answer i got for the 2nd part, i've realised is wrong. so i've changed it.)

4. For part a)

If you want the present value, then it is good.

For b)

I assume she made the down payment, you have to accumulate the 10 missed payment using the future value forumla :

$FV = 315 * \left[ \frac{(1.0067)^{10}-1}{0.0067} \right]=3246.69$

Now remeber that this formula gives you what she owe at time 10 not eleven,
accumulate it one time :

3246.69(1.0067) = 3268.64$Now this is the tricky part, we have accumulated this amount at time eleven and she is to make a payment a time 11, hence use the annuity due formula to get the present value of all the future payment (26 payments): $PV = 315 * \left[ \frac{1-(1.0067)^{-26}}{0.0067} \right](1.0067)=7543.58$ Add the PV and the FV = 10812.02$

5. Originally Posted by Stev381
For part a)

If you want the present value, then it is good.

For b)

I assume she made the down payment, you have to accumulate the 10 missed payment using the future value forumla :

$FV = 315 * \left[ \frac{(1.0067)^{10}-1}{0.0067} \right]=3246.69$

Now remeber that this formula gives you what she owe at time 10 not eleven,
accumulate it one time :

3036.97(1.0067) = 3268.44$Now this is the tricky part, we have accumulated this amount at time eleven and she is to make a payment a time 11, hence use the annuity due formula to get the present value of all the future payment (26 payments): $PV = 315 * \left[ \frac{1-(1.0067)^{-26}}{0.0067} \right](1.0067)=7543.58$ Add the PV and the FV = 10812.02$
In this line: 'Now remeber that this formula gives you what she owe at time 10 not eleven,
accumulate it one time :

3036.97(1.0067) = 3268.44\$'
where
did you get the 3,036.97 from??

6. wow I was lost this moring it should read as now edited.