# On September 20 th, Hope Hardware received an invoice for 26 items at $234 each with terms 5/10, 3/20, N/30 EOM. Hope Hardware reduced the bill by $1,990 on the last day of the first discount...

On September 20 th, Hope Hardware received an invoice for 26 items at $234 each with terms 5/10, 3/20, N/30 EOM.

Hope Hardware reduced the bill by $1,990 on the last day of the first discount period. A cheque for $1,478 arrived on the last day of the second discount period. A payment to completely pay off the remainder of the invoice arrived on the final day before a penalty would have been incurred.

a) What was the amount of the first payment?

$ ____________

b) What was the outstanding balance after the first payment was made?

$ ____________

c) What was the amount credited for the cheque for $1,478 when it was received during the second discount period?

$ ____________

d) What was the amount of the last payment to pay off the invoice completely?

$ ____________

e) What was the due date for the final payment? (Choose Month-Enter Date)

__________ ____________

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### 1 Answer

The invoice for 26 items worth $234 each, amounts to 26*234=$6084 in total.

The terms 5/10, 3/20, n/30 means the entire balance is due within 30 days after the end of the month in which the invoice is issued, but the buyer can take a 5% cash discount if the bill is paid within 10 days and a 3% discount if the bill is paid within 20 days after the end of the month in which the invoice is issued.

The invoice issue date is Sep 20.

Hope Hardware reduced the bill by $1,990 on the last day of the first discount period.

a) Let the actual amount of the first payment be $x

Then `x*6084/(0.95*6084) =1990`

`rArr x=1990*5779.8/6084=$1890.5`

b) The outstanding balance after the first payment was $(6084-1990)=$4094

A cheque for $1,478 arrived on the last day of the second discount period.

c) The amount credited at this point was 1478/0.97=$1523.7

d) The amount of the last payment to pay off the invoice completely was (4094-1523.7)=$2570.3

e) The last date for the final payment was October 30.