Math 253 -Theory of Interest
Assignment #6 - Due Nov 2 4pm
- Calculate the present value of an annuity on Jan 1, 2000, which pays $1000 per year starting Jan 1, 2001, and increases by $100 per year up to and including the last payment on Jan 1, 2014.
- Calculate the accumulated value of the annuity in question 1 on January 1 2015..
3. Find the present value of an annuity, which starts at $1 per year (payable at the end of the year) and increases by 1 per year to a value of $15, then decreases by $1 per year to the final payment of $1.
4. Calculate the present value of a perpetuity of $5 per year payable at the end of the year, increasing by $1 each year to a value of $25 per year, and then remaining at that level forever.
5. Redo questions 1 and 2 with an annual increase of 3% per year instead of $100.
6. Smith buys a perpetuity, which pays $8000 every three years with the first payment 5 years from now. Payments increase by 3 % each time starting with the second payment. Calculate the cost.
7.A ten-year annuity provides payments every 6 months (first payment 6 months from now). The first payment is 1 and increases by 2 percent every year. (Every second payment, first increase 18 months from now.) . The annual rate of interest is 6%. Calculate the cost of the annuity.
8. A ten-year annuity provides payments every 6 months (first payment 6 months from now). The first payment is $100 and increases by $10 every year. (Every second payment, first increase 18 months from now). The annual rate of interest is 6%. Calculate the accumulated value of the annuity on the date of the last payment.