Question

Please help me with this geometric/arithmetic sequence problem. Questions are in the comments. Willing to give a medal!!!

Answer 1

Clara wants to buy some land. She can choose between two different payment options.
Both options require her to pay for the land in 20 monthly installments.
Option 1: The first installment is $2500. Each installment is $200 more than the one before.
Option 2: The first installment is $2000. Each installment is 8 more than the one before.
(a) If Clara chooses option 1,
(i) write down the values of the second and third installments;
(ii) calculate the value of the final installment;
(iii) show that the total amount that Clara would pay for the land is $88 000.

(b) If Clara chooses option 2,
(i) find the value of the second installment;
(ii) show that the value of the fifth installment is $2721.

(c) The price of the land is $80 000. In option 1 her total repayments are $88 000 over the 20 months. Find the annual rate of simple interest which gives this total.

(d) Clara knows that the total amount she would pay for the land is not the same for both options. She wants to spend the least amount of money. Find how much she will save by choosing the cheaper option.