You have just started your first job and you want to have the basic appliances (fridge, washer, dryer, etc.) in your apartment. You face the following choices: (i) Purchase all appliances at the store using a bank loan. There is no down payment as the bank can take your appliances if you default on the loan. The loan is at the annual market rate of 9%, and the loan amount is $8,400 to be repaid monthly over 4 years. (ii) Rent-to-buy from the same store. The monthly rental is $185 for 48 months and then you pay $800 to own all the appliances. What is the net cost today of the cheapest option? (Enter just the number in dollars without the $ sign or a comma and round off decimals to the closest integer, i.e., rounding $30.49 down to $30 and rounding $30.50 up to $31.)
You can only compare "monies" if they are in the same "time" on your time-line.
I would use the present as the reference point.
Present Value of option I is $8400
(Clearly if you just paid them 8400, it's all done, right?
PV of option II , i = .09/12 = .0075 , n = 48
= 185 ( 1 - 1.0075^-48)/.0075 + 800(1.0075)^-48
= 7434.1846 + 558.8913
= $7993.08
So what do you think?
That is correct.
To find the net cost today of the cheapest option, we need to calculate the total cost for each option and compare them.
Option (i) involves purchasing all appliances using a bank loan. The loan amount is $8,400 to be repaid monthly over 4 years at an annual interest rate of 9%. We can use the formula for the monthly payment on a loan to find the total cost. The formula is:
Total Cost = Monthly Payment * Number of Payments
The monthly payment can be calculated using the loan amount, annual interest rate, and number of payments. In this case, the number of payments is 4 years * 12 months per year = 48 months.
Let's calculate the monthly payment for option (i):
Monthly Payment = $8,400 / [12 * 4] = $175
Total Cost for option (i) = $175 * 48 = $8,400
Option (ii) involves renting appliances for 48 months and then paying $800 to own them. Let's calculate the total cost for option (ii):
Rental cost = $185 * 48 = $8,880
Total Cost for option (ii) = Rental cost + $800 = $8,880 + $800 = $9,680
Therefore, the net cost today of the cheapest option is the total cost. Since option (i) has a total cost of $8,400 and option (ii) has a total cost of $9,680, the cheapest option is option (i).
So, the net cost today of the cheapest option is $8,400.
To calculate the net cost today of each option, we need to consider the cost of purchasing the appliances using a bank loan and the cost of renting-to-buy.
Option (i): Purchasing all appliances using a bank loan:
The loan amount is $8,400, and it will be repaid monthly over 4 years, which is 48 months. The annual interest rate on the loan is 9%, which means a monthly interest rate of 9% / 12 = 0.75%.
To calculate the monthly repayment amount, we can use the formula for calculating loan payments, which is:
Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Number of months))
Plugging in the values, we get:
Monthly payment = (8400 * 0.75%) / (1 - (1 + 0.75%)^(-48))
Calculating this using a financial calculator or spreadsheet, the monthly payment comes out to approximately $203.
Option (ii): Renting-to-buy from the same store:
The monthly rental cost is $185 for 48 months, and then there is an additional payment of $800 to own all the appliances.
To calculate the net cost today, we need to calculate the present value of the future rental payments and the additional payment. We can discount each future payment using the market rate of 9%. The formula for calculating the present value of an annuity is:
Net cost today = (Payment * (1 - (1 + Monthly interest rate)^(-Number of months))) / Monthly interest rate
Plugging in the values, we get:
Net cost today = (185 * (1 - (1 + 0.75%)^(-48))) / 0.75% + 800
Calculating this, the net cost today comes out to approximately $7,127.
Comparing the two options, the net cost today of the cheapest option is $7,127.