DP Mathematics: Applications and Interpretation 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 $x$.

Find an approximation for the real interest rate for the money invested in the account.

Find the value of her investment after a period of $5$ years.

Hence find the real value of Sophia’s investment at the end of $5$ years.

Calculate the amount Pietro will have in his account after $5$ years. Give your answer correct to $2$ decimal places.

Tommaso wants to invest his money in an account such that his investment will increase to $1.5$ times the initial amount in $5$ years. Assume the account pays a nominal annual interest of $r\%$ compounded quarterly.

Determine the value of $r$.

Estimate the value of Roger’s laptop after $5$ years.

Comment on the validity of your answer to part (b).

Find the value of $k$.

Calculate the value of Daisy’s investment after $2$ years.

Write down the amount of the loan.

the amount of interest paid by Daisy.

Find the amount of Daisy’s final payment.

Find how much money Daisy saved by making one final payment after $5$ years.

Find the minimum value of $m$, where $m\in \mathrm{\mathbb{N}}$.

the annual interest rate of the loan.

Using your answers to parts (a) and (b)(i), calculate how much interest they will have paid in total during the first $10$ years.

Find the amount Raul and Rosy will still owe the bank at the end of the first $10$ years.

Find the amount they will pay the bank each month.

For option 2, find the minimum value of $x$ that Juliana would need to invest each year. Give your answer to the nearest dollar.

For option 1, determine the minimum amount Juliana would need to invest. Give your answer to the nearest dollar.

Describe what the value in part (d)(i) represents in this context.

Calculate the value of $\underset{n=1}{\overset{10}{\text{Σ}}}\left(625\times 1.{064}^{\left(n-1\right)}\right)$.

Find the total amount paid for the car.

Bryan’s car depreciates at an annual rate of 25 % per year.

Find the value of Bryan’s car six years after it is purchased.

State which option Bryan should choose. Justify your answer.

Find the repayment made each quarter.

Find the interest paid on the loan.

State which option Bryan should choose. Justify your answer.

Find the total amount paid for the car.

Find the annual interest rate, $r$.

Bryan chooses option B. The car dealership invests the money Bryan pays as soon as they receive it.

If they invest it in an account paying 0.4 % interest per month and inflation is 0.1 % per month, calculate the real amount of money the car dealership has received by the end of the 6 year period.

Find the amount to be borrowed for this option.

Find the repayment made each quarter.

Find the amount to be borrowed for this option.

Find the annual interest rate, $r$.

Find the interest paid on the loan.

Calculate the value of her savings after 10 years.

The rate of inflation during this 10 year period is 1.5% per year.

Calculate the real value of her savings after 10 years.

Calculate the value of r.

Calculate 14 000 USD in INR.

Calculate the amount of this investment, in INR, in this account after five years.

Harinder chose option B. At the end of five years, Harinder converted this investment back to USD. The exchange rate, at that time, was 1 USD = 67.16 INR.

Calculate how much more money, in USD, Harinder earned by choosing option B instead of option A.

Complete the second column of the table by giving one example of a number from each set.

Josh states: “Every integer is a natural number”.

Write down whether Josh’s statement is correct. Justify your answer.

Calculate the value of Siân’s investment after four years. Give your answer correct to two decimal places.

After the four-year period, Siân withdraws $40000$ AUD from her savings account and uses this money to buy a car. It is known that the car will depreciate at a rate of $18$ % per year.

The value of the car will be $2500$ AUD after $t$ years.

Find the value of $t$.

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

Find the amount Phil would owe the bank after 20 years. 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

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

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

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.