What is the present worth of these future payments? (a) $25,500 eight years from now at 12% com-pounded annually. (b) $58,000 twelve years from now at 4% com-pounded annually. (c) $25,000 nine years from now at 6% compounded annually. (d) $35,000 four years from now at 9% compounded annually.

Question

Business

Trinity Davenport

26 March, 10:43

What is the present worth of these future payments? (a) $25,500 eight years from now at 12% com-pounded annually. (b) $58,000 twelve years from now at 4% com-pounded annually. (c) $25,000 nine years from now at 6% compounded annually. (d) $35,000 four years from now at 9% compounded annually.

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Answers (1)

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Kyle Maynard · Answer 1

a. PV = $10,299.02

b. PV = $36,226.63

c. PV = $14,797.46

d. PV = $24,794.88

Explanation:

To solve this question, we use present value formula

PV = C / (1+r) ^n

Where PV = Present value of a lump sum

C = Future amount to be discounted

r = Interest rate

n = Number of years

a. PV = C / (1+r) ^n

C = $25,500

r = 12%

n = 8

PV = $25,500 / (1+12%) ^8

PV = $25,500 / (1+0.12) ^8

PV = $25,500 / (1.12) ^8

PV = $25,500 / 2.475963176

PV = $10,299.02231

PV = $10,299.02

b. PV = C / (1+r) ^n

C = $58,000

r = 4%

n = 12

PV = $58,000 / (1+4%) ^12

PV = $58,000 / (1+0.04) ^12

PV = $58,000 / (1.04) ^12

PV = $58,000 / 1.601032219

PV = $36,226.62888

PV = $36,226.63

c. PV = C / (1+r) ^n

C = $25,000

r = 6%

n = 9

PV = $25,000 / (1+6%) ^9

PV = $25,000 / (1+0.06) ^9

PV = $25,000 / (1.06) ^9

PV = $25,000 / 1.689478959

PV = $14,797.46159

PV = $14,797.46

c. PV = C / (1+r) ^n

C = $35,000

r = 9%

n = 4

PV = $35,000 / (1+9%) ^4

PV = $35,000 / (1+0.09) ^4

PV = $35,000 / (1.09) ^4

PV = $35,000 / 1.41158161

PV = $24,794.88239

PV = $24,794.88