Calculating x with an Annuity and Annual Rate of 44%”

[yume]

A car is purchased by 12 million by paying 48 monthly fee due to x each quarterly fee due and 400 000 each for four years .

If a rate of 44% effective annual, determine the value of x .

Answer from textbook is $353 137.09

Ussualy, in problems I've seen, annuity is separated, but here is combine.
I tried solving by present and future value, but i always get a negative value, and really far from the answer.

 

[Wilmer]

A car is purchased by 12 million by paying 48 monthly fee due to x each quarterly fee due and 400 000 each for four years .

If a rate of 44% effective annual, determine the value of x .

Answer from textbook is $353 137.09

Ussualy, in problems I've seen, annuity is separated, but here is combine.
I tried solving by present and future value, but i always get a negative value, and really far from the answer.

Looks like you mean loan is repaid with 48 monthly payments of x
plus 16 quarterly payments of 400,000, at 44% effective annual.

Step 1:
Set up quarterly rate to result in 44% effective annual:
(1 + i)^4 = 1.44 ; you'll get i = .095445115...

Step 2:
u = PV of the 400,000 quarterly payments using above rate

Step 3:
Set up monthly rate to result in 44% effective annual:
(1 + i)^12 = 1.44 ; you'll get i = .03085332...

Step 4:
Calculate monthly payment required to repay (12,000,000 - u)
over 48 months using above rate