3. A saver wants $100,000 after ten years and believes that it is possible to earn an annual rate of 8 percent on invested funds.

a) What amount must be invested each year to accumulate $100,000 if (1) the payments are made at the beginning of each year or (2) if they are made at the end of each year?

b) How much must be invested annually if the expected yield is only 5 percent?

14. You invest $1,000 a year for ten years at 6 percent and then invest $2,000 a year for an additional ten years at 6 percent. How much will you have accumulated at the end of the 20 years?