Financial Applications (DP IB Applications & Interpretation (AI): HL): Exam Questions

In this question, give all answers correct to two decimal places.

Daniel and Jonah have each been given $5000 to save for university.

Daniel invests his money in an account that pays a nominal annual interest rate of 2.24%, compounded quarterly.

Calculate the amount Daniel will have in his account after 8 years.

Jonah wants to invest his money in an account such that his investment will double in 10 years. Assume the account pays a nominal annual interest rate of $r$%, compounded half-yearly.

Find the value of $r$.

Alice buys a new coffee machine for $4499. The value of the coffee machine depreciates by 9% each year.

Find the value of the coffee machine after 5 years. Give your answer correct to 2 decimal places.

Find the number of years and months it will take for the value of the coffee machine to be approximately $999.

The shop offers Alice a finance option in the form of a 1 year loan. Terms of the loan are:

• a 17.2% nominal annual interest rate, compounded monthly

• repayments to be made each month

Find the cost of each monthly repayment. Give your answer correct to 2 decimal places.

A new car costs $20 000 and its value depreciates to $14 792 after 2 years.

Calculate

(i) the annual rate of depreciation of the car

(ii) the value of the car after 5 years. Give your answer correct to 2 decimal places.

Find the number of years and months it will take for the car’s value to be approximately $4000.

Gus purchases the new car from a dealership who offers him a finance option in the form of a 3 year loan. Terms of the loan are:

• a 9% nominal annual interest rate, compounded monthly

• repayments to be made each month

Find the monthly repayment that would have to be made. Give your answer correct to 2 decimal places.

In this question, give all answers to two decimal places.

Biddy decides to purchase a new van from a dealership which costs $18 000, however she cannot afford the full amount.

The dealership offers her a finance option in the form of a 4 year loan. Terms of the loan are:

• a 12% nominal annual interest rate, compounded quarterly

• a 15% deposit

• repayments to be made each quarter

Calculate the loan amount Biddy would receive.

(i) Find the repayment that would have to be made each quarter.

(ii) Find the total amount paid for the van.

In this question, give all answers to two decimal places.

On his 40th birthday, Robert invests $15 000 into a savings account that pays a nominal annual interest rate of 4.78%, compounded monthly.

(i) Write an expression for the total value of the investment after $n$ years.

(ii) Find the total amount in the savings account after 3 and 5 years.

Find the age Robert will be when the amount of money in his account is 1.5 times the initial amount.

A second savings account pays a nominal annual interest rate of $r$%, compounded quarterly. If Robert had invested the $15 000 in this account instead, it would have earned the same amount of interest over 5 years.

Find the value of $r$.

Fraser decides to invest in a retirement plan for 25 years. In this plan, he will deposit $500 at the end of every month, on which he will receive 5.5% nominal annual interest, compounded monthly.

Find the value of the investment at the end of the 25 years. Give your answer correct to 2 decimal places.

After the 25 year period, Fraser will start receiving regular monthly payments of $1250. Assume that the investment earns no further interest once the payments begin.

Find the number of years it will take for Fraser’s monthly retirement payments to match the total value of the investment at the end of the 25 years.

Find the number of years it will take for Fraser’s monthly retirement payments to match the total amount he invested.

In this question, give all answers to two decimal places.

Lily takes a mortgage of $220 000 to purchase a house at a nominal annual interest rate of 4.18%, compounded monthly. She agrees to pay the bank $1600 at the end of every month to amortise the loan.

Find

(i) the number of years and months it will take Lily to pay back the loan

(ii) the total amount Lily will pay to purchase the house.

Lily wants to pay off the loan within 10 years.

Calculate the new monthly payment required to do this.

Georgia buys a new computer for herself that costs $1099. At the same time, she buys her son, Duncan, a new gaming computer that costs $2749.

It is anticipated that Georgia's computer will depreciate at a rate of 11% per year, whereas Duncan's gaming computer will depreciate at 18% per year.

Estimate the value of Georgia's computer after 6 years.

Georgia and Duncan's computers will have the same estimated value $k$ years after they were purchased.

Find:

(i) the value of $k$

(ii) the estimated value after $k$ years.

Aaron has been renting out his apartment for $1200 per month, however he wants to renovate the apartment to increase the monthly rent to $1750. He notifies his current tenants and they agree to move out. The renovations are expected to take 5 months.

Calculate the amount of rental income Aaron is foregoing by deciding to renovate the apartment.

Aaron takes out a loan of $25 000 to renovate the apartment. Terms of the loan are

• A nominal annual interest rate of 6.2%, compounded monthly

• Monthly repayments of $850.

Calculate the total amount paid for the renovations.

Aaron has some new tenants ready to move in as soon as the renovations are finished.

Find the number of months it takes for the increase in Aaron’s rental income to match the amount paid for the renovations, found in part (b).

John has just retired at the age of 65. He has $445 000 in his savings fund. He “rolls over” the money into an annuity fund which returns a nominal annual interest rate of 4.17%, compounded quarterly.

John decides to withdraw $2200 every month to live on.

Find the number of years and months for the money in the fund to run out.

After 5 years, John wants to make a withdrawal from his annuity to invest in a new online educational platform. Terms of the annuity state John is allowed to withdraw up to 9.5% of his account value without paying a surrender charge.

Calculate the maximum amount John can withdraw so that he does not have to pay the surrender charge.

Ben and Evan are twins and both receive €44 000 on their 21st birthday. Ben deposits his €44 000 into a savings account that pays a nominal annual interest rate of 3.27%, compounded annually. Evan invests his €44 000 into a fixed income fund that returns €1750 per year.

Calculate:

(i) the amount of interest that Ben earns if his sum is invested for 20 years, giving your answer to 2 decimal places

(ii) the amount of interest that Evan earns for his investment if invested for 20 years.

Find the number of complete years after which the amount in Ben’s account first exceeds the amount in Evan’s account.

Emily decides to buy a new boat at a cost of $20 000, but cannot afford the full amount. The boat dealership offers two options to finance a loan.

First option:

A 5 year loan at a nominal annual interest rate of 15%, compounded monthly. No deposit required and repayments are made each month.

Find the repayment made each month.

Second option:

A 5 year loan at a nominal annual interest rate of $r$% compounded quarterly. Terms of the loan require a 5% deposit and a monthly repayment of $400.

Find the annual interest rate, $r$.

State which option Emily should choose. Justify your answer.

Sasha takes out a loan of $19 800 to purchase new tools for his gardening business. He agrees to pay the bank $840 at the end of every quarter to amortise the loan. The loan has a nominal annual interest rate of 4.34%, compounded semi-annually.

Find the number of years it will take Sasha to pay back the loan.

Calculate the total amount that Sasha will pay in amortising the loan.

The bank offers Sasha an option to make a higher quarterly repayment of $980.

Calculate how much Sasha will save if he decides to make the higher payment.

Joshua wants to invest in Blueprint Construction LTD and so decides to buy 55% of the business for $660 000.

Calculate the total value of Blueprint Construction LTD.

Stephanie, Joshua’s financial advisor, has prepared the following table detailing the 5-year expected annual returns from Joshua’s investment in different economic states (boom or bust) and the probability of each state occurring.

Calculate the 5-year expected return of Joshua’s investment in Blueprint Construction LTD.

In 5 years, Blueprint Construction is valued at $1 800 000.

Find:

(i) the value of Joshua’s stake in Blueprint Construction LTD

(ii) the average annual return over the 5-year period.