Question

The Downers Grove Reporter ran an ad for a used 1998 Harley-Davidson Sportster 883 for $6,750. Patrick Schmidt is interested in the motorcycle but does not have the money right now. Patrick contacted the owner on October 19, and he agreed to give Patrick a loan plus 5.5% exact interest. The loan must be paid back by December 22 of the same year. The First National Bank will lend the $6,750 at 5%. Patrick would have 3 months to pay off the loan.

(a) What is the total amount Patrick will have to pay the owner of the motorcycle assuming exact interest?
(b) What is the total amount Patrick will have to pay the bank?
(c) Which option offers the most savings to Patrick?
(d) How much will Patrick save?

Answer 1

Total he has to pay owner=$7121.25

b). Total amount he has to pay the bank=$7087.50

c). Since borrowing from the bank is cheaper than borrowing from the owner,he would save more if he just borrows from the bank.

d). The amount he saves=(7121.25-7087.50)=$33.75

Step-by-step explanation:

a). Total he has to pay owner=Amount loaned+5.5% exact interest

where;

Amount loaned=$6,750

5.5% exact interest=(5.5/100)×6750=$371.25

Replacing;

Total he has to pay owner=(6750+371.25)=$7121.25

b). Amount he has to pay the bank

Total amount he has to pay the bank=Amount loaned+5% interest

where;

Amount loaned=6750

Interest=5%=(5/100)×6750=337.5

Replacing;

Total amount he has to pay the bank=(6750+337.50)=$7087.50

c). Since borrowing from the bank is cheaper than borrowing from the owner,he would save more if he just borrows from the bank. For example;

Total he pays the bank=$7087.50

Total he pays the owner=$7121.25

Get the difference=(7121.25-7087.50)=$33.75

Borrowing from the bank he saves $33.75 in comparison to borrowing from the owner

d). The amount he saves=(7121.25-7087.50)=$33.75