Mr Wilson wants to start a scholarship where the top student each year receives a \$4000 prize. If the interest on the initial investment averages 4\% per annum, compounded annually, how much should his initial investment be?
Sunil wants to make an ongoing donation of \$4300 to World Vision each year. If the interest on the initial investment averages 2.15\% per annum, compounded annually, how much should his initial investment be?
Ashleigh invests his superannuation payout of \$220\,000 in a perpetuity that pays 6\% per annum, compounded annually. What is the size of the annual payment he will receive?
Samih has just won a \$5\,000\,000 jackpot and decides to invest it in a perpetuity that pays 3\% per annum, compounded monthly. What is the size of the monthly payment he will receive?
Fraser invests his workers' compensation payout of \$2\,760\,000 in a perpetuity that pays 2.85\% per annum, compounded quarterly. What is the size of the quarterly payment he will receive?
Jenny receives \$600\,000 from an inheritance and wishes to invest the money so that her interest payments cover her monthly living expenses of \$1500 per month.
Find the annual interest rate, r, compounded monthly, that she will need for this investment.
Glen won the lotto and has invested the money in a perpetuity paying 8\% per annum compounded quarterly. He is able to pay himself \$25\,000 every quarter from his account without using any of the principal. How much money did he win?
Kathleen sets up a perpetuity with \$200\,000 invested at 6.1\% per annum, compounded annually. At the end of each year she donates a constant amount to one of the local charities in her area.
How much should she donate each year if she wishes to be able to do so indefinitely?
After a few years she plans a trip of a lifetime for her and her family and withdraws \$90\,000 from this account. How much will she now be able to donate each year to a local charity indefinitely?
Harriet invests her superannuation payout of \$500\,000 into a perpetuity with an interest rate of 9\% per annum compounded annually. This will provide her with a monthly income without using any of the initial investment.
Complete the following table:
| \text{N} | \text{I}\% | \text{PV} | \text{Pmt} | \text{FV} | \text{P/Y} | \text{C/Y} |
|---|---|---|---|---|---|---|
| 1 |
Hence, determine Harriet's monthly payment.
A university mathematics faculty has \$30\,000 to invest in a perpetuity. They intend to award an annual mathematics prize of \$1500 with the interest compounded per annum from the investment.
Complete the following table:
| \text{N} | \text{I}\% | \text{PV} | \text{Pmt} | \text{FV} | \text{P/Y} | \text{C/Y} |
|---|---|---|---|---|---|---|
| 1 |
Hence, determine the annual interest rate required.
\$16\,000 is invested in a perpetuity at 3\% per annum, compounded annually. A constant amount is withdrawn from the account at the end of each year.
Find the recursive rule that gives the balance of the account, A_{n+1}, at the end of year n+1.
\$30\,000 is invested in a perpetuity at 6\% per annum, compounded monthly. A constant amount is withdrawn from the account at the end of each month.
Find the recursive rule that gives the balance of the account, A_{n+1}, at the end of year n+1.
\$400\,000 is invested in an account at 4\% per annum, compounded annually. \$33\,000 is withdrawn from the account at the end of each year.
Write a recursive rule that gives the balance of the account, A_{n+1}, at the end of year \\ n+1.
Determine the amount remaining in the account at the end of 13 years.
What amount should be withdrawn each year so this investment is a perpetuity?
\$300\,000 is invested in an account at 6\% per annum, compounded annually. \$18\,000 is withdrawn from the account at the end of each year.
Write a recursive rule that gives the balance of the account, A_{n+1}, at the end of year \\ n+1.
Determine the amount remaining in the account at the end of 12 years.
Does this investment represent a perpetuity? Explain your answer.
\$150\,000 is invested in an account at 7.2\% per annum, compounded monthly. \$1200 is withdrawn from the account at the end of each month.
Write a recursive rule that gives the balance of the account, A_{n+1}, at the end of month n+1.
Determine the amount remaining in the account at the end of 29 months.
What amount should be withdrawn each month so this investment is a perpetuity?
Xavier invests \$350\,000 in a perpetuity earning 9.6\% per annum compounded monthly and wishes to make monthly donations to the Cancer Council for research.
How much should he donate to the Cancer Council each month if he wishes to be able to do so indefinitely?
After 3 years, Xavier experiences some financial difficulty and needs to withdraw \$3600 each month from this account to pay for living expenses and therefore he stops donating money to the Cancer Council.
Write a recursive rule that gives the balance of the account, A_{n+1}, at the end of the \\ (n+1)th month after he stops donating money.
Use the sequence facility on your calculator to determine at the end of which month his money will run out.