Calculate the amount of capital which is outstanding on 1st Jan 2033 in the case of an amortized loan of €250,000 repayable monthly in arrears over 30 years, where drawdown was 1st Jan 2020 and the first payment was made on 31st Jan 2020. The nominal annual rate of interest being applied is fixed at 6.0%, convertible monthly.

To provide for his grandson during 4 years of college, a businessman enters into an agreement with a financial institution. For a fee of €9000, the company offers to pay the student €200 at the end of each of the next 48 months. Calculate the effective annual rate of interest being used by the financial institution in making this offer.

Order the following series of cash flows using net present value and a positive rate of interest, from largest to smallest. Explain the logic (without calculation) for the ordering you choose. • A receipt of €2400 today; • A receipt of €2400 at the end of a period of 1 year from today; • A receipt of €200 at the start of each of 12 months from today; • A receipt of €200 at the end of each of 12 months from today.

Describe what is meant by the internal rate of return of a series of cash flows.

A government scheme requires those who partake to pay €500 at the end of each month, for a period of 60 months. In return, the investor receives 25% added by the government to the top of their own monthly contribution. At the end of the scheme, a single payment equal to the accumulated value of a series of monthly investments of €625 (the €500 + 25%, made at the time of payment of the €500) with interest applied at a fixed nominal annual rate of 1.2% convertible monthly, is returned to the investor.

• Calculate the accumulated value at the end of five years, which will be paid to the investor.

• Write down the amount and timing of all payments and receipts involved in this scheme for the individual.

• Calculate the internal rate of return on this investment.