Question

Find the following values:

a. The future value of a lump sum of $6,000 invested today at 9 percent, annual compounding for 7 years.

b. The future value of a lump sum of $6,000 invested today at 9 percent, quarterly compounding for 7 years.

c. The present value of $6,000 to be received in 7 years when the opportunity cost (discount rate) is 9%, annual compounding.

d. The present value of $6,000 to be received in 7 years when the opportunity cost (discount rate) is 9% quarterly compounding.

e. What is the effective annual rate (EAR) if the stated rate is 10% and compounding occurs monthly?

f. What is the present value of an ordinary annuity who pays $1,500 per year for ten years at 8 percent?

g. What is the present value of an annuity due who pays $1,500 per year for ten years at 8 percent?

h. What is the future value of an ordinary annuity who pays $1,500 per year for ten years at 8 percent?

i. What is the future value of an annuity due who pays $1,500 per year for ten years at 8 percent?

Answer 1

a. Answer: $ 10,968.23

Future value = Principal x ( 1 + r ) ⁿ = $ 6,000 x ( 1.09 ) ⁷ = $ 10,968.23

b. Answer: $ 11,187.27

Future value = $ 6,000 x ( 1.0225) ²⁸ = $ 11,187.27

c. Answer: $ 3,282.21

Present value = Future Value / ( 1 + r ) ⁿ = $ 6,000 / ( 1.09) ⁷ = $ 3,282.21

d. Answer: $ 3,217.94

Present value = $ 6,000 / ( 1.0225) ²⁸ = $ 3,217.94

e. Answer: 10.47 %

EAR = [ 1 + 0.10/ 12 ] ¹² -1 = 0.1047 or 10.47 %

f. Answer: $ 10,065.12

Present value for 10 years at 8 percent = $ 1,500 x [ { 1 - 1/ ( 1.08 ) ¹⁰ } / 0.08 ] = $ 10,065.12

g. Answer: $ 10,870.33

Present value of annuity due = $ 10,065.12 x 1.08 = $ 10,870.33

h. Answer: $ 21,729.84

Future value of ordinary annuity = $ 1,500 x [ {( 1.08 ) ¹⁰ - 1 } / 0.08 ] = $ 21,729.84

i. Answer: $ 23,468.23

Future value of annuity due = $ 21,729.84 x 1.08 = $ 23,468.23