Time value of money and interest rates

Your company in Ireland is buying a machine. The supplier offers two deals: pay €1,000,000 today, or €270,000 at the end of each of the next 4 years. Your company can borrow at 5% a year, so that is the rate at which you value money over time.

Your bank is reviewing its savings range against three rival accounts. Marketing wants to claim your new account beats “the best of them”, so you need to know which really pays the most over a year.

A UK insurer has agreed to pay an injury claim in 6 years. The amount is £5,000,000 in today's money and will rise with prices, expected to grow 2.5% a year. The insurer discounts at a nominal rate of 4.5%.

Your company places $25,000,000 on deposit with a bank from 15 March to 15 September 2027 at 4.8% a year. Dollar deposits use ACT/360 and simple interest.

A couple in Auckland can afford NZ$3,000 a month on a 30-year mortgage. The bank's rate is 6.6% a year, compounded monthly, with payments at the end of each month.

Your firm will need to borrow for one year starting two years from now, and the board wants to know what rate today's market implies for that loan. Government spot rates (annual compounding) are 1-year 4.0%, 2-year 4.4% and 3-year 4.6%. Ignore your credit spread.

A pension fund owes two lump sums, each worth £10,000,000 today at a 4% discount rate: one due in 5 years and one in 25 years. The risk committee asks what happens to their value if the whole yield curve rises by 1 percentage point.