DP Mathematics: Analysis and Approaches Questionbank

Calculate the value of Imon’s investment after $5$ years.

At the end of the $5$ years, Imon withdrew $x \text{SGD}$ from the fixed deposit account and reinvested this into a super-savings account with a nominal annual interest rate of $5.7\%$, compounded half-yearly.

The value of the super-savings account increased to $20 000 \text{SGD}$ after $18$ months.

Find the value of $x$.

For the value of $N$ found in part (c) (i), state Helen’s annual salary and Jane’s annual salary, correct to the nearest dollar.

Find Jane’s total earnings at the start of her $10$th year of employment. Give your answer correct to the nearest dollar.

Show that $H_n=2400n+67 600$.

Find the value of $N$.

Given that $J_n$ follows a geometric sequence, state the value of the common ratio, $r$.

Find the value of Amelia’s investment after $5$ years to the nearest hundred dollars.

Determine the number of years required for Amelia’s investment to reach the target.

Show that Chris will never reach the target if his initial deposit is $\$9000$.

Bill invests his $\$9000$ in an account that offers an interest rate of $r\%$ per annum compounded monthly, where $r$ is set to two decimal places.

Find the minimum value of $r$ needed for Bill to reach the target after $10$ years.

Find the amount Chris needs to deposit initially in order to reach the target after $5$ years. Give your answer to the nearest dollar.

Find the amount that Sam will have in his account after $10$ years.

Find the value of $r$ required so that the amount in David’s account after $10$ years will be equal to the amount in Sam’s account.

Find the interest David will earn over the $10$ years.

Find Gemma’s annual salary for the year 2021, to the nearest dollar.

Find the value of r, giving your answer to four significant figures.

Laurie makes no further deposits to or withdrawals from the account.

Find the year in which the amount of money in Laurie’s account will become double the amount she invested.

Calculate the original price of the bicycle.

Calculate the difference between the original price of the bicycle and the total amount Juan will pay.

Determine the amount that he will have in his account after 3 years. Give your answer correct to two decimal places.

Find the difference between the cost of the bicycle and the amount of money in Tommaso’s account after 3 years. Give your answer correct to two decimal places.

After $m$ complete months Tommaso will, for the first time, have enough money in his account to buy the bicycle.

Find the value of $m$.

Given that Phil’s aim is to own the house after 20 years, find the value for $P$ to the nearest dollar.

Show that the total value of Phil’s savings after 20 years is $\frac{({1.02}^{20}-1)P}{(1.02-1)}$.

Find the amount Phil would owe the bank after 20 years. Give your answer to the nearest dollar.

Hence or otherwise, find the minimum value of $Q$ that would permit David to withdraw annual amounts of $5000 indefinitely. Give your answer to the nearest dollar.

David wishes to withdraw $5000 at the end of each year for a period of $n$ years. Show that an expression for the minimum value of $Q$ is

$\frac{5000}{1.028}+\frac{5000}{{1.028}^2}+\dots +\frac{5000}{{1.028}^n}$.

Karl decides to donate this interest to a charity in France. The charity receives 170 euros (EUR). The exchange rate is 1 USD = t EUR.

Calculate the value of t.

Write down the amount of interest he earned after 5 years.

Calculate the amount of money he has in the account after 5 years.

Write down the amount of money Jashanti saves per month.