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larisa [96]
3 years ago
12

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]3 years ago
3 0

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

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Explanation:

The premium or discount as a percent of NAV will be calculated thus:

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