Question

Money is worth 1% per month to you. You're offered the following deals to buy your new Cadillac CTS.

Deal A	Deal B
Pay no money down	Pay X amount down today
Pay $800 per month for 12 month	Pay $1,000 per month for 60 months
Pay $1,000 per month for the second year
Pay $1,100 per month for years 3,4, and 5
You own the car!	You own the car!

What is the amount X that you must pay down to make Deal A and Deal B equivalent? Use compound monthly.

Answer 1

ANSWER:

In order to find x , we need to equate the pw of both deal a and b equal.

i = 1% per month and n = 5 years

pw of deal a = monthly pay in year 1(p/a,i,12) + monthly pay in year 2(p/a,i,24) - monthly pay in year 2(p/a,i,12) + monthly pay in year 3 to 5(p/a,i,60) - monthly pay in year 3 to 5(p/a,i,24)

pw of deal a = 800(p/a,1%,12) + 1000(p/a,1%,24) - 1000(p/a,1%,12) + 1100(p/a,1%,60) - 1100(p/a,1%,24)

pw of deal a = 800 * 11.255 + 1000 * 21.243 - 1000 * 11.255 + 1100 * 44.955 - 1100 * 21.243

pw of deal a = 9004 + 21,243 - 11,255 + 49,450.5 - 23,367.3

pw of deal a = $45,075.2

pw of deal b = x + monthly down payment for 5 years(p/a,i,n)

monthly down payment = $1000

i =1% per month

n = 60 months

pw of deal b = x + 1000(p/a,1%,60)

pw of deal b = x + 1000 * 44.955

pw of deal b = x + 44,955

now we will equate the pw of both the deals equally to find x

45,075.2 = x + 44,955

x = 45,075.2 - 44,955

x = $120.2