What is the present worth of these future payments? (a) $25,500 eight years from now at 12% com-pounded annually. (b) $58,000 tw

Question

3 years ago

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What is the present worth of these future payments? (a) $25,500 eight years from now at 12% com-pounded annually. (b) $58,000 tw

elve 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.

Business

1 answer:

grin007 [14] · Answer 1 · 2022-01-28T16:18:06+03:00

Answer:

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