Question

The Data

• Lightning Wholesale has opted to only carry two ski brands in 2014: Ogasaka and Nordica.

• The list prices for Ogasaka and Nordica are $840.00 and $800.00, respectively.

• The typical monthly compounded interest rates charged by the retailers are 6%, 8.5%, 12%, and 16%.

• Lightning Wholesale recommends a 10% down payment on all finance plans for all of its retailers.

Important Information

• All retailers sell the skis at the list price.

• All ordinary payment plans are either six month or nine month.

• Lightning Wholesale ignores sales taxes in its chart since every province has varying rates.

Your Tasks

1. For both product lines and for each interest rate, develop both a six-month and a nine-month payment plan amount chart that the retailers can advertise that incorporates the required down payment. For these advertised amounts, assume the final payment remains the same as all other payments (in application, though, the retailers will need to be cautioned that the final payment may be different and adjusted as needed, to which Lightning Wholesale can provide the necessary information as required).

2. Retailers ask you how to adjust the advertised payment plan chart amounts if they decide to sell the skis for some price other than the list price. What would you recommend? Provide calculations to support your answer.

3. Some retailers charge different interest rates and want to know if it is possible to just proportionally adjust the payment plan chart. For example, if a retailer charges 9% interest, this approach would then be to increase the 6% payment by 50% of the difference between the 6% and 12% level. Can retailers adjust your payment plan table in this way? Provide calculations using the provided numbers to support your answer.

4. Some retailers offer a 12-month payment plan and ask if it is possible to just take the six-month payment numbers and divide by 2, or take the nine-month payment numbers and divide by 3/4 to arrive at the 12-month payment plan numbers. Can retailers adjust your payment plan table in this way? Provide calculations to support your answer.

can you tell me the answers asap

Answer 1

The problem is basically for calculating equated monthly installments with different interest rates and tenor.

The formula to calculate equated monthly installments is :

[P x R x (1+R)^N]/[(1+R)^N-1]

where P = Principal

R = Rate of interest

N = Number of months

Ans 1:

Thus, the table for 6 months and 9 months can be calculated for both products by inputting the numbers in the formula and obtaining:

Table

Down payment : 84 $ Ogasaka

Down payment : 80$ Nordica

		6	months
Loan		6%	8.50%	12%	16%
756	Ogasaka	153.74	166.02	183.88	205.17
720	Nordica	146.42	158.12	175.12	195.40
		9	months
756	Ogasaka	111.15	123.55	141.89	164.11
720	Nordica	105.86	117.67	135.13	156.30

Payments to be made respectively at above value for 6 months/9 months as per the plan.

Ans 2

To change the values, the tables can be provided for a $100 list price and any other list price can then be configured by dividing the value by 100 and multiply the same by the figure in the table.

Table for $ 100 list price will be:

	6	months
Loan	6%	8.50%	12%	16%
90	18.30	19.76	21.89	24.43
	9	months
90	13.23	14.71	16.89	19.54

Wherein the downpayment will be $10.

For example suppose list price for Ogasaka is kept at 900$

then down payment = 900*0.1 = 90$

And say 9 month plan with 6% is taken then equated value to be paid per month will be:

900/100*13.23 = 119.08

Ans 3:

Let us prepare the similar table for 6%, 9% and 12% for a $100 list price for 6 months,

the value will be:

	6	months
Loan	6%	9.00%	12%	16%
90	18.30	20.06	21.89	24.43

Thus, if a retailer decides to give at 9% and tries to derive the value from 6% and 12% then:

18.3 + (21.89-18.3)/2 = 18.3+1.79 = 20.09 which is approximately equal to the 9% value in the table and thus retailer can use this logic.

Ans 4:

Let us prepare a 12 month table, 6 month table and 9 month table for a single rate say 6%:

Loan	Months	6%
90	6	18.30
90	9	13.23
90	12	10.73

If 6 month is being tried to be extended to 12 months by dividing the value by 2 : 18.3/2 = 9.15 < 12 month payment plan, this is because compounding effect is removed, the interest is being charged for more months and thus value for 12 month is higher and thus retailer cannot use it.

For 9 months value to convert into 12 months: 3/4*13.23 = 9.9225

The value is still lesser and thus this cannot be used by retailers.