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

  • Thread starter Thread starter yume
  • Start date Start date
  • Tags Tags
    Annuity Rate
yume
Messages
1
Reaction score
0
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.
 
Mathematics news on Phys.org
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
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
Back
Top