Question

franchise. AMOUNT OF AN ANNUIY Find the amount of an if $250/month is paid into it for a period of 20 Vr. ity 1 con- ing interest at the rate of 8%/year compounded tinuously 12. THE AMOUNT OF AN ANNUITY Find the amount of an annu- ity if $400/month is paid into it for a period of 20 yr, ean- ing interest at the rate of 6%year compounded con- tinuously 13. THE AMOUNT OF AN ANNUITY Aiso deposits $150/month in a savings account paying 6%/year compounded continu- ously. Estimate the amount that will be in his account after 15 yr 14. CUSTODIAL ACCOUNTS The Armstrongs wish to establish a custodial account to finance their children's education. If they deposit $200 monthly for 10 yr in a savings account paying 6%/year compounded continuously, how much will their savings account be worth at the end of this period? 15. IRA AccOUNTS Refer to Example 4, page 470. Suppose Marcus made his IRA payment on April 1, 1994, and annu ally thereafter. If interest is paid at the same initial rate. approximately how much did Marcus have in his account at the beginning of 2010? 16. PRESENT VALUE OF AN ANNUITY Estimate the present value of an annuity if payments are $800 monthly for 12 yr and the account earns interest at the rate of 5%/year con- pounded continuously. 17. PRESENT VALUE OF AN ANNUITY Estimate the present vab an annuity if payments are $1200 monthly for 15 yr and e account earns interest at the rate of 6%year con- pounded continuously. 18. LOTTERY PAYMENTS A state lottery commissioneall winner of the "Million Dollar lottery 20 annes ments of $50,000 each, If the prevailingnrt valu 6%! crest rate is year compounded continuously, find the pres of the winning ticket. wishes to supple- $300/month for the met 19. REVERSE ANNUITY MORTGAGES Sinclair w ment his retirement income by 0 yr. He plans to obtain a reverse annuity

Answer 1

As per rules I am answering the first 4 subparts of the question

11: FV = CF*( e^rt -1)/ (e^r -1)

= 250*(2.718^((0.08/12)*20*12)-1)/ (2.718^0.08/12-1)

=147,729.80

12: FV= CF*( e^rt -1)/ (e^r -1)

r= 6% pa = 0.5% per month

t= 20*12 = 240 months

FV= 400*(2.718^(0.005*240)-1)/(2.718^0.005-1)

=185132

13: FV= CF*( e^rt -1)/ (e^r -1)

r= 6% pa = 0.5% per month

t= 15*12 = 180 months

FV= 150*(2.718^(0.005*180)-1)/(2.718^0.005-1)

=43676.39

14: FV= CF*( e^rt -1)/ (e^r -1)

r= 6% pa = 0.5% per month

t= 10*12 = 120 months

FV= 200*(2.718^(0.005*120)-1)/(2.718^0.005-1)

=32801.50