Find the nominal annual discount rate convertible monthly equivalent to an effective annual interest rate of 10%. (ii) Find the annual effective interest rate equivalent to a discount rate of 8% pa convertible quarterly. 9. £250 is invested at a discount rate of 18% pa convertible monthly for the first 3 months followed by an interest rate of 20% pa convertible quarterly for the next 9 months. Calculate the accumulated sum at the end of the year. 10. Under its current rent agreement, a company is obliged to make annual payments of £7,500 for the building it occupies. Payments are due on 1 January 2006, 1 January 2007 and 1 January 2008. If the company wishes to cover these payments by investing a single sum in its bank account that pays 7.5% pa compound, what sum must be invested on 1 January 2005? 11. A company expects to receive for the next five years a continuous cashflow with a rate of payment of 100 x 0.8º at time (years). Calculate the present value of this cashflow assuming a constant force of interest of 8% pa. 12. Calculate a25 and 15 at 13% % pa effective 13. Calculate ST and 5₁3 at 31% pa effective. 14. Find the present value as at 1 January 2005 of a series of 10 annual payments starting at £500 on 1 January 2006 and increasing by £100 each year. Assume an effective rate of interest of 8% pa. 15. Calculate the present value at time 0 of payments of £50 at time 0, £60 at time 1, £70 at time 2 and so on. The last payment is at time 10. Assume that the annual effective rate of interest is 4.2%. 16. A man makes payments into an investment account of $200 at time 5, $190 at time 6, $180 at time 7, and so on until a payment of $100 at time 15. Assuming an annual effective rate of interest of 3.5%, calculate: (i) the present value of the payments at time 4 (ii) the present value of the payments at time 0 (iii) the accumulated value of the payments at time 17. Calculate the present value as at 1 January 2003 of an annuity payable annually in arrear for 15 years. The first payment is 500 and subsequent payments increase by 3% per annum compound. Assume effective rates of interest of 10% per annum.