Answer all the questions
Q1 An annuity pays $200 at the end of each month for 5 years, and $300 at the end of each month for the next 5 years. Find the discounted value of the annuity at 12% compounded continuously. Ans. $16 370.16 Q2 Is it cheaper to buy a car for $9800 and after 3 years trade it in for $2000, or to rent a car for $250 a month payable at the end of each month for 3 years? Assume that maintenance and license costs are identical for both alternatives and that money is worth j1 = 8%. Ans. Renting is cheaper. Q3 A property worth $80 0000 is sold for $10 000 down and equal monthly payments for the next 20 years. Find the monthly payment if the interest rate is j1 = 8.14%. Ans. $579.04 Q4 A couple would like to accumulate $20 000 in 3 years as a down payment on a house, by making deposits at the end of each week in an account paying interest at 712 = 6%. Find the weekly deposit, assuming that compound interest is paid for any part of a conversion period. Ans. $117.11 Q5 A deposit of $2000 is made to open an account on April 1, 1992. Quarterly deposits of $300 are then made for 5 years, the first deposit on July 1, 1992. Starting on October 1, 1998, the first of a sequence of $1000 quarterly withdrawals is made. Assuming interest at 10% compounded continuously, find the balance in the account (a) on October 1, 1995; (b) on October 1, 2001. Ans. (a) $7804.35; (b) $2058.21Q6 The Andersons can buy a certain house listed at $100 000 and pay $35 000 down. They can get a mortgage from the bank for $65 000 at j2 = 12%, payable over 25 years in monthly installments. The seller of the house offers the house for $105 000; he will give them a $70 000 mortgage at 12 = 10%, payable monthly, and will assume a 25-year amortization period. If the two interest rates are guaranteed for 25 years, what should the Andersons do? Ans. Take the seller's offer. Q7 Mr. X has a $50,000 mortgage with monthly payments over 25 years at j2=10%. Because they get paid weekly, they decide to switch to weekly payments (still at j2=10% and for 25 years). Compare their weekly payments to monthly payments. (Ans. $102.89 weekly, $447.24 monthly) Q.8 An annuity consists of 60 payments of $200 at the end of each month. Interest is at j1= 11.05%. Find the value of this annuity (a) at the time of the first payment, (b) 2 years before the first payment, (c) at the time of last payment. Ans. 9380.77, 7606.79, 15705. Q9. A college graduate must repay the government $4200 for outstanding student loans. The grad. nate can afford to pay $150 monthly. If the first payment is made at the end of the first year and money is worth 11% compounded quarterly, find the number of full payments required and the size of the smaller concluding payment. Ans. 36, $71.19 1 L.. 01 monthlu a Q10. The proceeds of $100 000 death benefit are left on deposit with an insurance company for seven years at an annual effective interest rate of 5%. The balance at the end of seven years is paid to the beneficiary in 120 equal monthly payments of X, with the first payment made immediately. During the payout period, interest is credited at an annual effective interest rate of 3%. Calculate X. Ans. $1352.74Q11 do part (a) only Find the discounted value of an ordinary simple perpetuity paying $400 a year, if interest is (@) 71 = 8%, (b) j1 = 12.48%. Ans. (a) $5000; (b) $3205.13 Q12 How much money is needed to establish a fund that pays a research scholarship of $10 000 each half-year, if the endowment can be invested at j2 = 10% and if the first scholarship will be provided (a) a half-year from now? (b) immediately? (c) Four years from now? Ans. (a) $200 000; (b) $210 000; (c) $142 136.27 Q13 The XYZ Company has a stock that pays a semiannual dividend of $4. If the stock sells for $64, (a) what yield j2 did the investor desire? (b) What is the equivalent rate ji? Ans. (a) 12.5%; (b) 12.89%Q14 lly A college estimates that its new campus center will require $3000 for upkeep at the end of each wear for the next 5 years and $5000 at the end of each year thereafter, indefinitely. If money is worth 12% effective, how large an endowment is necessary for the future upkeep of the campus center? Ans. $34 457.12 Q15 A perpetuity pays $4000 per year, as follows: in odd-numbered years, a payment of $4600 is made at the end of the year. in even-numbered years, a payment of $1000 is made at the end of each quarter. Interest is at annual effective rate of 8%. At the beginning of an odd-numbered year, this perpetuity is exchanged for another of equal value which provides semiannual payments, the first payment due six months hence. What is the semiannual payment of the new perpetuity? Ans. $1989.36
