Question

Of the following car financing options, which one would you prefer while assuming that you prefer paying the least amount of dollars and that you face a 10% annual compound interest rate on all your financial decisions?

********I'm looking for a break down for each option here************

A payment $10,000 today and another of $10,000 in one year from today.

A lump-sum payment of $19,000 today only.

A lump-sum payment of $20,000 in two years from today.

A lump-sum payment of $20,000 today only.

Answer 1

The present value is computed as follows:

= Future value / (1 + r)ⁿ

Present value of option 1 is as follows:

= $ 10,000 + $ 10,000 / 1.10 (Present value payment of $ 10,000 today will be $ 10,000 since the same is paid today)

= $ 19,090.91 Approximately

Present value of option 2 is as follows:

= $ 19,000 (Present value payment of $ 19,000 today will be $ 19,000 since the same is paid today)

Present value of option 3 is as follows:

= $ 20,000 / 1.10²

= $ 20,000 / 1.21

= $ 16,528.93 Approximately

Present value of option 4 is as follows:

= $ 20,000 (Present value payment of $ 20,000 today will be $ 20,000 since the same is paid today)

Since the cost of present value of option 3 is the least, hence option of A lump-sum payment of $20,000 in two years from today is the correct option.