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 5%, and the loan amount is $6,000 to be repaid monthly over 4 years.(ii) Rent-to-buy from the same store. The monthly rental is $125 for 48 months and then you pay $1,000 to own all the appliances. What is the net cost today of the cheapest option?
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To determine the net cost today of each option, we need to calculate the total amount of money you will spend in both cases. Let's break down the calculations for each option:
Option (i) - Purchase all appliances using a bank loan:
- Loan amount: $6,000
- Loan period: 4 years (48 months)
- Annual interest rate: 5%
To calculate the monthly payment on the loan, we can use the formula for a fixed monthly payment on an installment loan:
Loan Payment = Loan Amount / Present Value Factor
Present Value Factor = (1 - (1 + r)^(-n)) / r
Where:
- r is the monthly interest rate (annual rate divided by 12)
- n is the total number of periods (loan period)
Calculating r:
Monthly interest rate = 5% / 12 = 0.004167
Calculating Present Value Factor:
PV Factor = (1 - (1 + 0.004167)^(-48)) / 0.004167
Next, we calculate the monthly loan payment:
Monthly Payment = $6,000 / PV Factor
Option (ii) - Rent-to-buy from the same store:
- Monthly rental cost: $125 for 48 months
- Lump-sum payment to own appliances: $1,000
To calculate the total amount spent on rent:
Rent Total = Monthly rental cost × Number of months
Finally, we compare the net cost today of both options. The net cost today is the total amount spent minus any money received:
Net Cost Today = (Total amount spent on option) - (Money received from option)
For Option (i), there is no money received, so the net cost today is simply the total amount spent.
For Option (ii), the total amount spent is the sum of the rent total and the lump-sum payment to own the appliances.
Total amount spent = Rent Total + $1,000
Comparing the net cost today for both options will tell us which option is cheaper.
To calculate the net cost today, we will need to substitute the given values into the formulas and perform the calculations as described above.