192 divided by 15 as a fraction of the remainder
1 answer:
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Answer:
a) $161.8
b i) Approximately 327.7 hours
ii) The cost of saving is less but the opportunity cost of saving can be higher with regards to technology and regulation
Step-by-step explanation:
The amount Mary would like to save, FV = $10,000
The time Mary over which Mary intends to save the amount, t = 5 years
Therefore, the number of monthly payments, n = 12
a) The amount in interest the bank pays compounding, i = 1.2% per annum
The amount that Mary will deposit each month is given as follows;
The compound interest formula is given as follows;
Where;
PMT = The monthly payment
Therefore, we get;
PMT = 10,000/((1 + 0.012/12)^(60) - 1)/(0.012/12)) ≈ 161.8
The amount she needs to deposit monthly, PMT ≈ $161.8
b i) Given that the minimum wage varies and we have a minimum wage here is officially approximately $79, which is 160 hours a month work
The number of hours work needed = 161.8/79 × 160 ≈ 327.7 hours a month approximately
b ii) Given that the interest rate for saving is lower than the interest rate for borrowing, the amount paid by saving is much lesser than the amount paid back when borrowing, therefore, it is more cost effective to save
However, while saving, changes may take place, such as the use of what is being saved for, therefore, it can be more beneficial to borrow and make use of the items now while they are still available and acceptable, such as the drive towards net zero is making fuel based cars less popular with the drive being towards electric cars.
If there are real roots to be found for this polynomial, the Rational Root Theorem and synthetic division are the best way to find them. I teach from a book that uses c and d for the possible roots of the polynomial. C is our constant, 2, and d is the leading coefficient, 1. The factors of 2 are +/- 1 and +/-2. The factors for 1 are +/-1 only. Meaning, in all, there are 4 possibilities as roots for this polynomial. But there are only 3 total (because our polynomial is a third degree), so we have to find the first one, at least, from our possibilities above. Let's try x = -1, factor form (x + 1). If there is no remainder when we do the synthetic division, then -1 is a root. Put -1 outside the "box" and the coefficients from the polynomial inside: -1 (1 2 -1 -2). Bring down the first coefficient of 1 and multiply it by the -1 outside to get -1. Put that -1 up under the 2 and add to get 1. Multiply 1 times the -1 to get -1 and put that -1 up under the -1 and add to get -2. -1 times -2 is 2, and -2 + 2 = 0. So we have our first root of (x+1). The numbers we get when we do the addition along the way are the coefficients of our new polynomial, the depressed polynomial (NOT a sad one cuz it hates math, but a new polynomial that is one degree less than that of which we started!). The new polynomial is 
. That can also be factored to find the remaining 2 roots. Use standard factoring to find that the other 2 solutions are (x+2) and (x-1). Our solutions then are x = -2, -1, 1, choice B from above.