Math Exam 4 CH. 14 Questions and How to answers

Find the total interest earned on the sinking fund in last example.

1) *Amount invested = $839.55(20 periods/payments) = $16,791* 2) *Total Interest = $25,000 - 16,791 = $8,209*

Erin Calipari plans to have a stream of $2,500 payments each year for two years at 8% annual interest. How much should she set aside today?

1) N = 1 * 2 = 2 periods/payments 2) R = 8% / 1 = 8% 3) Table Value = 1.783 4) *Present Value =($2,500)(1.783)= $4,457.50*

Find the present value of an ordinary annuity with annual payments of $680 at 9% annual interest for 25 years?

1) N = 1 * 25 = 25 periods 2) R = 9% / 1 = 9% 3) Table Value = 9.823 4) *Present Value = (680)(9.823) = $66,79.64

Jane Watson is contributing $3,000 each year to a Roth IRA. The Roth IRA earns 3% per year. How much will she have at the end of 25 years? A Roth IRA contribution is made as the fund is established, so it is an annuity due.

1) N = 1 year * 25 years = 25 periods 2) R = 3% / 1 = 3% 3) Table Value = 36.459 4) *FV = (3,000)(36.459)(1 + 0.03) = $112,658.31*

Find the future value of an annuity due of $12,000 annually for three years at 3% annual interest. How much was invested? How much interest was earned?

1) N = 1 year * 3 years = 3 periods 2) 3% / 1 = 3% (3.00%) --> 0.03 (keep in decimal form) 3) Table Value = 3.091 4) FV = $12,000(3.091)(1+0.03) = $38,204.76 5) *Amount Invested = 12,000 x (1)(3) = $36,000* 6) *Total Interest = $38,204.76 - 36,000 = $2,204.76*

Marvin Murphy contributes $400 per month to a payroll deduction 401(k) at work. His employer matches his contribution up to $200 per month. If the fund averages 6% per year, compounded monthly, how much will be in the account in 10 years?

1) N = 12 monthly * 10 years = 120 periods 2) R = 6% * / 12 monthly = 0.5% = 0.005 3) Table value = 163.879 4) *FV = (600)(163.879)(1 + 0.005) = $98,327.41*

Matthew Bennett recognizes the value of saving part of his income. He has set a goal to have $25,000 in cash available for emergencies. How much should he invest semiannually to have $25,000 in ten years if the sinking fund he has selected pays 8% annually, compounded semiannually?

1) N = 2 * 10 = 20 periods/payments 2) R = 8% / 2 = 4% 3) Table Value = 0.0335818 4) *Sinking fund = 25,000(0.0335818) = $839.55*

Find the future value of an ordinary annuity of $6,500 semiannually for seven years at 6% annual interest compounded semiannually? How much was invested? How much was earned?

1) N = 2 * 7 = 14 periods 2) R = 6% / 2 semiannually = 3% (3.00%) 3) Table Value = 17.086 4) FV = $6,500(17.086) = $111,059 5) *Amount Invested = ($6,500)(2)(7) = $91,000* 6) *Total Interest = 111,059 - 91,000 = 20,059*

What semiannual sinking fund payment would be required to yield $48,000 nine years from now? The annual interest rate is 6% compounded annually.

1) N = 2 * 9 = 18 periods 2) R = 6% / 2 = 3% 3) Table Value = 0.0427087 4) *Sinking fund payment = $4,800 (0.0427087) = $2,050.02*

Find the future value of an annuity due of $750 semiannually for four years at 8% annual interest compounded semiannually. What is the total interest earned?

1) N = 2 years * 4 years = 8 periods 2) R = 8% / 2 = 4% - 0.04 (keep in decimal form) 3) Table Value = 9.214 4) FV = (750) x (9.214) x (1 + 0.04) = $7,186.92 5) Total Invested = 750(8 periods) = $6,000 6) *Total interest = $7,186.92 - $6,000 = $1,186.92*

Janice and Terry Van Dyke have decided to establish a quarterly ordinary annuity of $3,000 for the next ten years at 8% annual interest compounded quarterly, How much should they invest in a lump sum now to provide the stream of payments?

1) N = 4 * 10 = 40 periods 2) R = 8% / 4 = 2% 3) Table Value = 27.335 4) *Present Value = 3,000(27.335) = $82,065*

Pat Lechleiter pays an ordinary annuity of $2,500 quarterly at 8% annual interest compounded quarterly to establish supplemental income for retirement. How much will Pat have available at the end of the year?

1) N = 4 * 5 = 20 periods 2) R = 8% / 4 quarterly = 2% (2.00%) 3) Table Value = $24,297 4) *FV = ($2,500)($24.297) = $60,742.50*

Dorothy Strawn has plans to invest $30,000 over five years in an annuity at 6% and she wants the best plan. Annuity 1 is a monthly ordinary annuity of $500 compounded monthly. Annuity 2 is a semi annual ordinary annuity of $3,000 compounded semiannually. Annuity 3 is a quarterly annuity due of $1,500 compounded quarterly. Annuity 4 is a yearly annuity due of $6,000 compounded annually. What annuity yields the greatest future value?

Annuity 1 ------------- N = 12 * 5 = 60 periods R = 6% / 12 = 0.5% Table Value = 69.770 Periodic Payment = $500 *FV = (500)(69.770) = $34,885* Annuity 2 ------------- N= 2 * 5 = 10 periods R = 6 % / 2 = 3% Table Value = 11.464 Period Payment = $3,000 *FV = (3,000)(11.464)= $34,392* Annuity 3 ------------- N = 4 * 5 = 20 R = 6% / 4 = 1.5% Table Value = 23.124 Periodic Payment = $1,500 *FV = ($1,500)($23,124)(1 + 0.015) = $35,206.29* Annuity 4 ------------- N = 1 * 5 = 5 periods R = 6% / 1 = 6% Table Value = 5.637 *FV = $6,000(5.637)(1+0.06) = $35,851.32* <-- greatest FV