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

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To determine the value of x for a car purchased at 12 million with a 44% effective annual rate, the problem involves both monthly and quarterly payments. The solution requires calculating the quarterly interest rate and the present value of the quarterly payments of 400,000. After establishing the necessary rates, the remaining balance after accounting for the quarterly payments is used to find the monthly payment x over 48 months. The textbook answer for x is $353,137.09. The complexity arises from combining annuity payments rather than separating them, which is common in similar problems.
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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.
 
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yume said:
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
 
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