Jackson wants to invest $10 000 for 5 years.a He could choose to earn simple interest paid at a rate of 4.5% per annum.(i) Determine how much he earns in interest each year.(ii) Write a recurrence relation to model the value of the investment fromyear to year. Let 𝑆𝑛 be the value after n years.(iii) Determine the value of the investment after 5 years.(iv) How much interest will Jackson earn over the five years

(i) To determine how much he earns in interest each year, we use the formula for simple interest which is I = PRT, where I is the interest, P is the principal amount (initial investment), R is the annual interest rate (in decimal form), and T is the time the money is invested for (in years).

In this case, P = $10,000, R = 4.5% = 0.045 (in decimal form), and T = 1 year.

So, I = PRT = $10,000 * 0.045 * 1 =$450.

Therefore, Jackson earns $450 in interest each year.

(ii) The recurrence relation to model the value of the investment from year to year would be S_n = S_(n-1) + $450, where S_n is the value after n years. This is because each year, the investment increases by the amount of the annual interest, which is$450.

(iii) To determine the value of the investment after 5 years, we use the recurrence relation from part (ii). We start with the initial investment of $10,000 and add the annual interest of$450 for each of the 5 years.

So, S_5 = $10,000 + 5 *$450 = $10,000 +$2,250 = $12,250.

Therefore, the value of the investment after 5 years is $12,250.

(iv) The total interest Jackson will earn over the five years is the difference between the final value of the investment and the initial investment.

So, total interest = S_5 - P = $12,250 -$10,000 = $2,250.

Therefore, Jackson will earn $2,250 in interest over the five years.