1. An investment scheme pays $200 at the end of each of the next 4 years, $400 at the end of year 5, $300 at the end of year 6 and $500 at the end of year 7. Given that other investments of equal risk earn 10% per annum, find out the present value and future value of this investment.
2. A loan of $100,000 with an interest rate of 10% per annum is to be paid off by 20 equal quarterly payments; the first payment is due today. Find the size of the quarterly payment.
3. Greg won a lottery of $200,000. He invested the entire amount and expects a yearly return of 10% per annum on his investment and he will receive 150 equal monthly payments. The first payment is expected in 2 years. Find the size of the payments.
4. Firm A pays 10% interest per annum, compounded on a quarterly basis. To remain competitive, the manager of another firm (Firm B) is willing to match the interest rate offered by Firm A, but interest will be compounded on a monthly basis. What nominal rate of interest must Firm B offer to its clients?
5. An amount of $28,974 is required at the end of 10 years from now, and regular contributions can be made into an investment scheme that pays 8% per annum (compounded annually):
i. What single payment could be made at the beginning of the first year to achieve this objective?
ii. What amount could you pay at the end of each year annually, for 10 years to achieve this same objective?