(Solved): (i) Find the nominal annual discount rate convertible monthly equivalent to an effective annual int ...

(i) 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 5?3 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.