The “car license tax” for plates ending in number 1 could be paid in cash until

Question

The “car license tax” for plates ending in number 1 could be paid in cash until 02/18/16, with 12% discount, or 05 monthly payments without interest, with 1st payment at the day 03.09.16. after calculating the rate effective monthly paid by person, find out if it is better to pay in cash or in 05 payments, inthe following conditions:

* for those who have money: money is invested with net yield of a 1% per month.

* for those who don’t have money: a loan is being offered for 6% effective interest per month.

Explanation / Answer

Lets assume tax is $100

Option 1: Paying using cash

So here customer can avail a discount of 12%, so effective payment = 100 * (1-12%) = $88

This has to be discounted for 9 days using 1% rate

PV = PV(1%,9/30,0,88,0) = $87.74

Here 1% is monthly effective interest rate

9/30 is number of days

0 is payment each month

88 is future value

0 is for making payments at end of month

Option 2: Monthly Payments

Lets Equal payment of $20 is made for 5 months

So PV can be calculated in an excel sheet as follows

PV=PV(6%,5,20,0,0) = $84.25

Here 6% is monthly effective interest rate

5 is number of payments

20 is payment each month

0 is future value

0 is for making payments at end of month

Since value of the payments is less in option 2, one should go for 5 monthly payments

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