Question

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One year ago Gena bought a water deionizer on an installment plan. The plan specified that
she make a down payment of $5,000 immediately, and pay installments of $8,000 after three
months and nine months. Gena made the down payment, but did not pay the $8,000
installments that were due nine months ago and three months ago. The seller agreed to
discharge Gena’s debt with a payment today, and a second payment six months from today.
Today’s payment will be $1,000 more than the payment six months from today. The interest
rate charged is 8% compounded quarterly. Suggested focal date:
today
.
You must include a
complete time-line diagram

Answer 1

: Interest of the due amount is calculated for the period from due date till today. Numbers are rounded to 2 decimal points wherever required.  

Complete Timeline

09-06-2018 (A Year ago) Gena made a down payment of $5000

09-09-2018 (Nine months ago) First installment (Say X) $8000 is due.

09-03-2019 (Three months ago) Second installment (Say Y) $8000 is due

09-06-2019 (Today) With interest rate 8% compounded quarterly

It has been three quarters since X is due, so it has to be compounded three times.

After one quarter X becomes $8000 + $640 = $8640, after two quarters it becomes $8640 + $691.20 = $9331.20 and after 3 quarters it will be $9331.2 + $746.5 = $10077.70.

it has been one quarter since Y is due so $640 is added only once. so Y becomes $8000 + 640 = $8640

So the total settlement made for Gena's debt is $10077.70 + $8640 = $18717.70

Given that today's payment (Say A) will be $1000 more than the payment (Say B) to be made six months from today.

A + B = 18717.70, A - B = 1000

2A = 19560

A = 9858.85 and B = 8858.85

09-06-2019 Today's payment is $9858 and 85 cents.

09-12-2019 Payment to do after six months is $8858 and 85 cents.

Thank you.