(1) A three-year continuous annuity pays a total of $100 during the first year, $400 duringthe second year, and $1,000 during the third year. Within each year, the payments aremade continuously and evenly throughout the year. The effective annual interest rate is10%. Find the present value of this annuity.

(2) At any moment t, a continuously-varying continuous 4-year annuity (between time t = 0and t = 4) makes payments at the rate of 4et per year at moment t. The force of interestis 10%. Find the present value of this annuity.

(3) At any moment t, a continuously-varying continuous 10-year annuity makes payments atthe rate of 10t per year at moment t. The force of interest also varies continuously,according to the formula t = 0.02t. Find the present value of this annuity.

(4) Suppose a project requires you to invest $30 now, and $12 two years from now. Theproject returns $40 one year from now. Find all the yield rates (internal rates of return)of this project. Then, find the range of annual effective interest rates which will producea net present value greater than zero.

(5) For an investment of $500 now and $1,000 five years from now, you can receive a 10-year $200 annual payment annuity, with the first payment occurring one year from now.The effective annual interest rate is 10%. Find the net present value of this investmentopportunity.

(6) What is the internal rate of return on a project that requires a $10,000 investment now,and provides returns to the investor of $6,000 one year from now and $6,000 two yearsfrom now?

(7) You make a one-time deposit of $1,000 into an account (Account A) which pays out 8%effective annual interest at the end of each year. Each year, you take the interest payoutand deposit it into an account (Account B) earning an effective annual interest rate of 5%.Find the total amount in the two accounts combined, 20 years after your original $1,000deposit.

(8) At the end of each year for 30 years, you deposit $2,000 into an account that earns aneffective annual interest rate of 6%. At the end of each year, you are paid the interestfrom this account, and you then reinvest that interest into a second account earning anannual effective interest rate of 4%. How much do you have in these two accounts,combined, after the 30 years?

(9) On 1/1/15 (month/day/year), you deposit $1,000 into a mutual fund. On 1/1/16, the valueof your fund is $800. On 1/1/17, the value of your fund is $1,200. On 1/1/18, the valueof your fund is $1,080. Find both the geometric and the arithmetic average annual ratesof return during your three-year investment period.

(10) On 1/1/15, you deposit $20,000 into an account. At the end of each of the next fourcalendar quarters, the value of the account and the deposit/withdrawal activity is asfollows:Date Account Value Activity 3/31/15 $ 22,000 $ 2,000 withdrawal 6/30/15 23,000 7,000 deposit 9/30/15 26,000 8,000 withdrawal12/31/15 21,000 -----(The account values represent the amount in the account immediately before thedeposit or withdrawal activity on that date.) Find both the time-weighted rate of returnand the dollar-weighted rate of return on the account during 2015.