(1) You want to accumulate $1,000,000 over the next 10 years. You intend to do this bymaking deposits of X into an investment account at the end of each month, for 30 years.The account earns i(4)= 10%. Find X.
(2) A 30-year annuity pays $1,000 semiannually (i.e., every six months). The interest rate isi(12)= 12%. Find the present value of this annuity 12 months prior to the first payment.
(3) A perpetuity will make payments of $50,000 every third year, with the first paymentoccurring three years from now. The effective annual interest rate is 8%. Find thepresent value of this perpetuity.
(4) You deposit money into an account each year for 20 years. The first deposit is $1,500,and then each subsequent annual deposit is $500 greater than the previous deposit. Theeffective annual interest rate is 10%. Find the accumulated value of your account, twoyears after the last (20th) deposit.
(5) A 30-year annuity is scheduled to make the following payments: $1,000 at the end ofeach of the first 20 years, and then payments at the end of years 21 through 30 are each$1,000 greater than the previous deposit. (Thus, the payment at t = 21 is $2,000, at t = 22is $3,0000, etc.) The annual effective interest rate is 12%. Find the present value of thisannuity two years before the first payment.
(6) A 10-year annuity makes payments at the end of each month. The first payment is$20,000, and thereafter each subsequent monthly payment is $100 less than the previous 2payment. The interest rate is 9% convertible monthly. Find the present value of thisannuity, one month prior to the first payment.
(7) A perpetuity makes quarterly payments, with the first payment being $1,000, and eachsubsequent payment being $250 greater than the previous payment. The effective annualinterest rate is 10%. Find the present value of this perpetuity one year before the firstpayment.
(8) A jury decides to award an injured person a series of payments to compensate her formedical costs stemming from a car accident. The injured person is entitled to a 30-yearannual-payment annuity that will pay $20,000 now, and then each subsequent annualpayment will be 3.5% higher than the previous year's payment (to offset future inflation).Assume that the effective annual interest rate is 8%. Find the present value, now, of thisannuity.
(9) Two growing perpetuities, each with annual payments, have the same yield rate (i.e., thesame interest rate applies to both). The first perpetuity has an initial payment of $1,000one year from now, and each subsequent annual payment increases by $200. The presentvalue of this first perpetuity is $38,290. The second perpetuity - a perpetuity-due - hasan initial payment of $750 now, and each subsequent annual payment increases by 4%.Find the present value, now, of the second perpetuity.
(10) Abby offers to pay you at the rate of $20,000 per annum, continuously, for the next 10years. Ben offers to pay you X at the end of each of the next 10 years. The force ofinterest applying to both offers is 10%. Find the value of X such that you are indifferentbetween these two offers.