(a) The amount of interest you will save on this loan if you make the partial payment and don't purchase the additional serving supplies is $553.80.
(b) The amount you will save by purchasing the discounted serving supplies and not making the partial payment is $2,946.20.
Step-by-step explanation:
Note: This question is note complete. The complete question is therefore presented before answering the question as follows:
You are the owner of four Taco Bell restaurant locations. You have a business loan with Citizens Bank taken out 60 days ago that is due in 90 days. The amount of the loan is $50,000, and the rate is 9.5% using ordinary interest. You currently have some excess cash. You have the choice of sending Citizens $35,000 now as a partial payment on your loan or purchasing an additional $35,000 of serving supplies such as food containers, cups, and plastic dinnerware for your inventory at a special discount price that is "10% off" your normal cost of these items.
(a) How much interest will you save on this loan if you make the partial payment and don't purchase the additional serving supplies?
(b) How much will you save by purchasing the discounted serving supplies and not making the partial payment?
Explanation of the answers is now given as follows:
(a) How much interest will you save on this loan if you make the partial payment and don't purchase the additional serving supplies?
Since an ordinary interest is used, it implies that the total interest amount has to be calculated based on a 360-day year instead of a 365-day year. Therefore, the the interest saved can be calculated as follows:
I_$50K = PRT (1)
Where,
I_50K = Total Interest on the original $50,000 loan = ?
P = Principal = $50,000
R = interest rate = 9.5%
T = Number of days in the loan period / 360 = (60 + 90) / 360 = 150 / 360 = 0.416666666666667
Substituting the values into equation (1), we have:
I_$50K = $50,000 * 9.5% * 0.416666666666667
I_$50K = $1,979.17
Daily interest on $50,000 loan = I_$50K / Number of days in the loan period = $1,979.17 / 150 = $13.19
Also, we have:
I_PB = PRT (2)
Where,
I_PB = Innterest on principal balance = ?
P = Principal balance = $50,000 - $35,000 = $15,000
R = interest rate = 9.5%
T = Number of days remaining / 360 = 60 / 360 = 0.166666666666667
Substituting the values into equation (2), we have:
I_PB = $15,000 * 9.5% * 0.166666666666667
I_PB = $237.50
Daily interest on principal balance = I_PB / Number of days remaining the loan period = $237.50 / 60 = $3.96
Daily interest to save = Daily interest on $50,000 loan - Daily interest on principal balance = $13.19 - $3.96 = $9.23
Interest amount to save on the loan = Number of days remaining * Daily interest to save = 60 * $9.23 = $553.80
Therefore, the amount of interest you will save on this loan if you make the partial payment and don't purchase the additional serving supplies is $553.80.
(b) How much will you save by purchasing the discounted serving supplies and not making the partial payment?
This can be calculated as follows:
Discount receivable from purchasing serving supplies = Cost of serving supplies * Discount rate = $35,000 * 10% = $3,500
Amount to save by purchasing serving supplies = Discount receivable from purchasing serving supplies - Interest payable on loan for the remaining 60 days (2)
Where;
Discount receivable from purchasing serving supplies = $3,500
Interest payable on loan for the remaining 60 days = Interest amount to save on the loan as calculated in part (a) = $553.80
Substituting the values into equation (2), we have:
Amount to save by purchasing serving supplies = $3,500 - $553.80 = $2,946.20
Therefore, the amount you will save by purchasing the discounted serving supplies and not making the partial payment is $2,946.20.
