Task 1

The Goal

Students will work with financial concepts to find the amount of investment that an individual can do over an amount of time.

Part I:

Ahmed,who is a grade 09 student, is planning to save money while he is studying at ATHS. Ahmed has 5,000 Dhs to start with, and he is planning to save 500 Dhs per month.

a.    What is the type of the sequence at which the money will grow?

arithmetic sequence.

b.    How much money will he save after 4 years?

12 months in a year => 12(4) = 48 months

a_n = a₁ +d(n-1)

a₄₈ = 5000 +500(48-1)

a₄₈ = 28500 AED

c.    His brother has borrowed from him some money, his brother agreed to pay 50 Dhs in the first month and 25 Dhs more in each of the following months; how much did Ahmed’s brother borrow knowing that it took him 1 year to pay his debt?  

                           

a_n = a₁ +d(n-1)

a₁₂ = 50 +25(12-1)

a₁₂ = 325 AED

Ahmed’s brother borrowed 325 AED.

d.    Let the amount saved at the end of the first year be a and the amount that was saved at the second year b, and the amount that was saved at the end of the fourth year c, find a relation between a,b and c ?

First year(a)=a₁₂ = a₁ +d(12-1)

a₁₂ = 5000 +500(12-1)

a₁₂ = 10500 AED

Second year(b)=a₂₄ = a₁ +d(12-1)

a₂₄ = 5000 +500(24-1)

a₂₄ = 16500 AED

Fourth year (c) = a₄₈₌ 28500 AED

The second year will be more than the first year by 6000 AED.

The difference between the second year and the Forth year is 12000 AED
The amount will increase each year by 6000 AED