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?

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

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

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

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

(Please show calculations of all options, that would help so much)

Answer 1

Option (A) is correct

Here we need to calculate the present value of all the options and select the lowest present value.

(A) Here we will use the following formula:

PV = FV / (1 + r%)n

where, FV = Future value = $20000, PV = Present value, r = rate of interest = 10%, n= time period = 1

Now,putting the values in the above equation, we get,

PV = $20000 / (1 + 10%)1

PV = $20000 / (1 + 0.10)

PV = $20000 / 1.10

PV = $18181.82

So, present value is $18181.82

(B) Present value of $10000 today is $10000 and present value of $10000 one year from today is:

PV = FV / (1 + r%)n

where, FV = Future value = $10000, PV = Present value, r = rate of interest = 10%, n= time period = 1

Now,putting the values in the above equation, we get,

PV = $10000 / (1 + 10%)1

PV = $10000 / (1 + 0.10)

PV = $10000 / 1.10

PV = $9090.91

So, total present value = $10000 + $9090.91 = $19090.91

(C) Present value of lump sum payment of $19000 today is $19000.

(D) Present value of lump sum payment of $20000 today is $20000.

Since the present value of option A i.e a lump sum payment of $20000 two years from today is lowest i.e. $18181.82. So, it should be preferred.