Question 0418

Arithmetic and Geometric Progressions (APs, GPs)

2018 Paper 1 Question 11 Variant

Question

Caleb invests his money with Company C, which allows him to invest

{\$50}

into a savings account on the first day of every month. At the end of each month, the total in the account is increased by

{a\%.}

(i)

It is given that

{a=0.9.}

(ia)

Caleb invests

{\$50}

on 1 January 2021. Write down how much this

{\$50}

is worth at the end of 31 December 2021.

[1]

(ib)

Caleb invests

{\$50}

on the first day of each of the 12 months of 2021. Find the total amount in the account at the end of 31 December 2021.

[3]

(ic)

Caleb continues to invest

{\$50}

on the first day of each month. Find the month in which the total in the account will first exceed

{\$2000.}

Explain whether this occurs on the first or last day of the month.

[5]

Deliah invests her money with Company D, which allows her to invest

{\$50}

on the first day of each month. Each

{\$50}

invested earns a fixed bonus of

{\$b}

at the end of every month for which it has been in the account. The accumulated bonuses do not earn any further bonus.

(iia)

Find, in terms of

{b,}

how much

{\$50}

invested on 1 January 2021 will be worth at the end of 31 December 2021.

[1]

(iib)

Deliah invests

{\$50}

on the first day of each of the 24 months in 2021 and 2022. Find the value of

{b}

such that the total value of all the investments including bonuses, is worth

{\$1350}

at the end of 31 December 2022.

[3]

It is given instead that ${a=2}$ for Company C.

(iii)

Find the value of

{b}

for Company D such that investing with both Company C and Company D will result in the same total value at the end of the

{72\textrm{th}}

month.

[3]