Question

# Find the following values: a. The future value of a lump sum of \$6,000 invested today...

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?

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

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

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

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

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

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

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

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

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

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