Question

You want to finance a car and Mango Bank offers you a 5% annual interest rate, and you have to pay $225 at the end of each month. Banana Bank offers you the same rate, but you have to pay $225 at the beginning of the month, in addition you have a final payment of $50. The period is five years (60 months) in both cases. What is the present value of either option, which option is better?

Answer 1

Present value of option mean present value of future monthly payment towards the loan.
In this case we would use present value of annuity formula (ordinary annuity - Payment is made at end of the year)
Present value of annuity	Monthly payment*(1-((1+r)^-n))/r
where r represents interest rate and n represents no of payments.
Monthly interest rate	0.42%	5%/12
Calculation of present value for option 1 offered by Mango Bank.
Present value of option	225*(1-((1+0.0042)^-60))/0.0042
Present value of option	225*52.9907
Present value of option	$11,922.91
Thus, present value of option offerred by Mango bank is $11,922.91.
Formula to calculate present value of option offerred by Banana bank.
Present value	Monthly payment + [Monthly payment*(1-((1+r)^-(n-1)))/r] + Final payment*(1/(1+r)^n)
Present value	225 + [225*(1-(1.0042^-59)))/0.0042]+[50*(1/1.0042^60)]
Present value	225 + [225*52.2115]+[50*0.779205]
Present value	$12,011.55
Thus, present value of option offerred by banana bank is $12,011.55.
Option offerred by Mango bank is better as in present value terms lower amount needs to be paid for car financing.