Question 0408

Arithmetic and Geometric Progressions (APs, GPs)

2008 Paper 1 Question 10 Variant

Question

(i)

Alex saves

{\$50}

on 1 January 2021. On the first day of each subsequent month, she saves

{\$25}

more than in the previous month, so that she saves

{\$75}

on 1 February 2021,

{\$100}

on 1 March 2021, and so on.
On what date will she first have saved over

{\$2500}

in total?

[5]

(ii)

Brie puts

{\$50}

on 1 January 2021 into an investment account which pays compound interest at a rate of

{5\%}

per month on the last day of each month. She puts a further

{\$50}

into the account on the first day of each subsequent month.

(iia)

How much compound interest has her original

{\$50}

earned at the end of

{2}

years?

[2]

(iib)

How much in total is in the account at the end of

{2}

years?

[3]

(iic)

After how many complete months will the total in the account first exceed

{\$2500?}

[4]