5-1A. (Compound interest) to what amount will the following investments accumulate?

a. $5,000 invested for 10 years at 10 percent compounded annually

5000 x (1.10)10 = 5000 x2.5937 =12968.5

b. $8,000 invested for 7 years at 8 percent compounded annually

8000 x(1.08)7 = 8000 x 1.7138 = 13710.59

c. $775 invested for 12 years at 12 percent compounded annually

775 x(1.12)12 = 775 x3.8959 =3019.38

d. $21,000 invested for 5 years at 5 percent compounded annually

21000 x (1.05)5 =21000x 1.2762 =26801.91

5-2A. (Compound value solving for n) How many years will the following take?

a. $500 to grow to $1,039.50 if invested at 5 percent compounded annually

500/1039.5 =.481

See .48 under 5% in pv of $1 table = 15 years .

b. $35 to grow to $53.87 if invested at 9 percent compounded annually

35/53.87 =.649

See .649 under 9% in pv of $1 table = 5 years

c. $100 to grow to $298.60 if invested at 20 percent compounded annually

100/298.6 =.3348

See .3348 under 20% in pv of $1 table = 6 years .

d. $53 to grow to $78.76 if invested at 2 percent compounded annually

53/78.76 =.6729

See .6729 under 2% in pv of $1 table = 20 years

5-3A. (Compound value solving for I) at what annual rate would the following have to be invested?

a. $500 to grow to $1,948.00 in 12 years

1948/500 = (1+r)12

12 under root 3.896 =1.12 =1.12-1 = .12 or 12%

Rate = 12%

b. $300 to grow to $422.10 in 7 years

422.1/300 = (1+r)7

7 under root 1.407 =1.05 =1.05-1 = .05 or 5%

Rate = 5%

c. $50 to grow to $280.20 in 20 years

280.2/50 = (1+r)20

20 under root 5.604 =1.09 =1.09-1 = .09 or 9%

Rate = 9%

d. $200 to grow to $497.60 in 5 years

497.6/200 = (1+r)5

5 under root 2.488 =1.2 =1.2-1 = .2 or 20%

Rate = 20%

5-4A. (Present value) what is the present value of the following future amounts?

a. $800 to be received 10 years from now discounted back to the present at 10 percent

800/(1.10)10 = 308.43

b. $300 to be received 5 years from now discounted back to the present at 5 percent

300/(1.05)5 = 235.05

c. $1,000 to be received 8 years from now discounted back to the present at 3 percent

1000/(1.03)8 = 789.41

d. $1,000 to be received 8 years from now discounted back to the present at 20 percent

1000/(1.2)8 = 232.56

5-5A. (Compound annuity) what is the accumulated sum of each of the following streams of payments?

a. $500 a year for 10 years compounded annually at 5 percent

500x{1.05)10-1}/.05 = 500x12.5778 =6289

b. $100 a year for 5 years compounded annually at 10 percent

100 x (1.10)5-1/.10 = 100 x 6.1051 =610.51

c. $35 a year for 7 years compounded annually at 7 percent

35 x (1.07)7-1/.07 = 35x 8.65 = 302.89

d. $25 a year for 3 years compounded annually at 2 percent

25 x (1.02)3-1/.02 = 25 x 3.06 = 76.51

5-6A. (Present value of an annuity) what is the present value of the following annuities?

a. $2,500 a year for 10 years discounted back to the present at 7 percent

2500 x {1-(1/1.07)10}/.07 = 2500 x 7.02 =17550

b. $70 a year for 3 years discounted back to the present at 3 percent

70 x {1-(1/1.03)3}/.03 = 70 x 2.8286 =198

c. $280 a year for 7 years discounted back to the present at 6 percent

280 x {1-(1/1.06)7}/.06 = 280 x 5.5823 =1563

d. $500 a year for 10 years discounted back to the present at 10 percent

500 x {1-(1/1.1)10}/.1 = 500 x 6.1445 =3072