Answer: = 10n - 111
Step-by-step explanation:
The first term of the sequence is - 101
we need to confirm that the sequence is arithmetic , that is , if it is arithmetic , it must have a common difference (d).
d = second term - first term = third term - second term
d = -91 - (-101)
d = -91 + 101
d = 10
Therefore the formula for the nth term is given as:
= a + (n - 1 ) d
= - 101 + (n - 1) 10
= - 101 + 10n - 10
= -111 + 10n
Therefore :
= 10n - 111
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.