Financial Maths — Question Bank

📖 Hover (or tap) any dotted word for its definition. Write your answers in the squared boxes with a pencil, finger or mouse — they save on your device.

2025 · Paper 1 · Q8 (a, b)part of 50Financial Maths

(a)Jacob buys a new kayak in a shop. The kayak is usually priced at €870. This price is reduced by 15% in a sale. Jacob gets a further reduction of 10% on this reduced price, because he is a member of the shop’s loyalty club. Find the price that Jacob pays for the kayak.

(a)

(b)Jacob buys a paddle online. The paddle costs $95. Jacob thinks that the exchange rate being used is €1 = $1·183. The actual exchange rate being used is €1 = $d, where d ∈ ℝ. As a result, the paddle costs €1·02 more than Jacob thought that it would. Use this to find the value of d, correct to 3 decimal places.

(b)

2024 · Paper 1 · Q750 marksFinancial Maths

(a)Fiadh has a gross annual salary of €54 000. She pays income tax at a rate of 20% on the first €40 000 of her salary and at a rate of 40% on the remainder. She has an annual tax credit of €1775. Work out her net annual pay, assuming that there are no other deductions.

(a)

(b)Fiadh and her partner take out a 25-year mortgage with a monthly interest rate of 0·279%. They make equal monthly repayments of €1647·75 at the end of each month. They make the first repayment exactly one month after they take out the mortgage.

(i)Write down the present value of each of their first three monthly repayments, at the time when they take out the mortgage. Give each value as a fraction. Do not multiply out any powers.

(b)(i)

(ii)Work out the amount of money that Fiadh and her partner borrowed for their mortgage. Give your answer correct to the nearest euro.

(b)(ii)

(c)Fiadh puts money in a savings account, and leaves it there for a number of years. The following expression gives F(t), the amount of money in the account in euro after t years, where t ∈ ℝ, t ≥ 0: F(t) = 5000 e^0·04t

(i)Use differentiation to find the rate at which the amount of money in the account is increasing after 3·5 years. Give your answer correct to the nearest euro per year.

(c)(i)

(ii)Use integration to find the average amount of money in the account over the first 5 years. Give your answer correct to the nearest euro.

(c)(ii)

(iii)Work out the annual rate of interest (AER) for this account. That is, find the percentage increase in the amount of money in the account over the course of one year. Give your answer as a percentage, correct to 2 decimal places.

(c)(iii)

2023 · Paper 1 · Q850 marksFinancial Maths

Olga, Chen, Fiona, and Rohan all have bank accounts.

(a)Olga puts €3000 in a savings account. Interest is added annually at a rate of 2·4% per year. Work out the amount in Olga's account after 5 years, correct to the nearest cent.

(a)

(b)(i) Explain what is meant by the present value of a payment of €1000 in 1 year's time, at a particular interest rate.

(b)(i)

(ii)Chen puts a different amount in a savings account with the same interest rate (2·4% per year). After 6 years, Chen has €4000 in the account. Work out how much money Chen put in the account initially, correct to the nearest cent.

(b)(ii)

(c)Fiona is taking out a loan at the same annual interest rate (2·4% per year). Fiona makes payments quarterly (4 times per year). Work out the quarterly interest rate that would be equivalent to an APR of 2·4%. Give your answer as a percentage, correct to 2 decimal places.

(c)

(d)Rohan wants to put the same amount of money in a savings account at the start of each month for 36 months so that, at the end of 3 years, he will have a total of €12 000 in the account. Interest is calculated at a rate of 0·11% per month.

(i)Taking €A to be the amount Rohan puts in his account at the start of each month, write down a geometric series in €A to show the total amount of money in the account at the end of the 3 years. Include the first two and the last two terms.

(d)(i)

(ii)Hence, find the value of €A that will give a total of €12 000 in the account after 3 years. Give your answer correct to the nearest cent.

(d)(ii)

(e)A park sells three types of ticket: child, student, and adult. The table gives the price of each ticket and the percentage of tickets sold (e.g. 15% of all tickets sold are student tickets). The expected value of the price of a ticket is €13·85. Work out the value of x, the price of an adult ticket.

Type of ticket	Child	Student	Adult
Price of ticket	€11	€5 less than an adult ticket	€x
Percentage	52%	15%	33%

(e)

(f)When an item is being sold: the mark up is the profit as a percentage of the cost price, and the margin is the profit as a percentage of the selling price. A shop sells an item with a margin of 18%. Work out the mark up for this item. Give your answer as a percentage, correct to the nearest percent.

(f)

2020 · Paper 1 · Q525 marksFinancial Maths

(a)A couple agree to take out a €250 000 mortgage in order to purchase a new home. The loan is to be paid back monthly over 25 years with the repayments due at the end of each month. The bank charges an annual percentage rate (APR) which is equivalent to a monthly rate of 0·287%. Using the amortisation formula, or otherwise, find the couples' monthly repayment on the mortgage. Give your answer in euro correct to the nearest cent.

(a)

(b)Another couple agree to take out a mortgage of €350 000, at a rate of 0·3% per month, in order to purchase a new home. This loan is also to be paid back monthly over 25 years with the repayments due at the end of each month. The amount of each repayment is €1771. After exactly 11 years of repayments, the couple receive a financial windfall. They decide to repay the remaining balance on the mortgage. Write down a series (including the first two and last two terms) which shows the total of the present values of all the remaining monthly repayments due over the remaining 14 years of the mortgage (after the last monthly repayment at the end of year 11). Hence, find how much the couple will need to repay in order to clear their mortgage entirely. Give your answer correct to the nearest cent.

(b)

2017 · Paper 1 · Q855 marksFinancial Maths

(a)When a loan of €P is repaid in equal repayments of €A at the end of each of t equal periods, where i is the periodic compound interest rate, the repayment is A = P i(1 + i)^t(1 + i)^t − 1. Show how this amortisation formula is derived. You may use the formula for the sum of a finite geometric series.

(a)

(b)Alex has a credit card debt of €5000. One method of clearing it is to make a fixed repayment at the end of each month equal to 2·5% of the original debt.

(i)What is the fixed monthly repayment, €A, required to pay the debt of €5000?

(b)(i)

(ii)The annual percentage rate (APR) charged on the debt is 21·75%, fixed. Find, as a percentage correct to 3 significant figures, the monthly interest rate equivalent to an APR of 21·75%.

(b)(ii)

(iii)Complete the table showing how the balance of the €5000 debt reduces each month for the first three months, assuming an APR of 21·75% charged and compounded monthly (Payment 1: previous balance reduced by 42·50, new balance 4957·50).

(b)(iii)

(iv)Using the formula you derived, or otherwise, find how long it would take to pay off the €5000 debt using this repayment method. Give your answer in months, correct to the nearest month.

(b)(iv)

(v)Alex decides instead to borrow €5000 from the Credit Union to pay off the credit card debt. The APR is 8·5% fixed, repaid in equal weekly repayments at the end of each week for 156 weeks. Find the amount of each weekly repayment.

(b)(v)

(vi)How much will Alex save by paying off the debt using the Credit Union loan instead of the fixed repayment from part (b)(i) to the credit card company?

(b)(vi)

2015 · Paper 1 · Q625 marksFinancial maths

A person borrows €200 000 to buy a house. The loan is to be paid back in equal monthly repayments over 20 years. The APR is 3%, fixed for the duration of the loan.

(a)Show that the monthly rate of interest which is equivalent to an APR of 3% is 0·246627%, correct to 6 decimal places.

(a)

(b)Find, correct to the nearest euro, the amount of each monthly repayment.

(b)

(c)After 10 years the person inherits some money and decides to pay off the full outstanding balance on the loan. Find, correct to the nearest euro, the outstanding balance at this point.

(c)

Questions reproduced from State Examinations Commission Leaving Certificate examination papers,
© State Examinations Commission (examinations.ie). Gathered here for study use.

Financial Maths Questions