A man was injured in an accident at work he receives a disability grant of R4800 in the first year. This grant increases with a fixes amount each year..
a). What is the annual increase if over 20 years he would have received a total of R143500
b). His initial annual expenditure os R2600 and increases at a rate of R400 per year after how many years does his expenses exceed his income
Well what did you pick and what do you have to do?
Well I'm kinda having a problem with application
a). To find the annual increase, we need to calculate the difference between the total amount received over 20 years (R143500) and the initial grant received in the first year (R4800).
Total increase over 20 years = R143500 - R4800 = R138700
Since the grant increases by a fixed amount each year, we can divide the total increase by the number of years to find the annual increase.
Annual increase = Total increase over 20 years / Number of years
Annual increase = R138700 / 20 = R6,935
Therefore, the annual increase is R6,935.
b). To determine the number of years when his expenses exceed his income, we need to find the point where his annual expenses surpass his annual income.
Let's set up an equation to solve for the number of years:
Initial income = R4800
Initial expenses = R2600
Expense increase per year = R400
Income - Expenses = 0 (when expenses exceed income)
(R4800 + Annual increase per year * Number of years) - (R2600 + Expense increase per year * Number of years) = 0
Simplifying the equation, we get:
R4800 + R6,935 * Number of years - (R2600 + R400 * Number of years) = 0
R2200 + R6535 * Number of years - R400 * Number of years = 0
Combining like terms, we get:
R6135 * Number of years - R400 * Number of years = -R2200
R5735 * Number of years = R2200
Number of years = R2200 / R5735
Number of years ≈ 0.383 years
Therefore, his expenses exceed his income after approximately 0.383 years, which is equivalent to around 4 months and 1 week.