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Taya2010 [7]
3 years ago
5

A coin sold at auction in 2017 for $1,965,500. The coin had a face value of $5 when it was issued in 1794 and had previously bee

n sold for $305,000 in 1971. a. At what annual rate did the coin appreciate from its first minting to the 1971 sale
Business
1 answer:
aksik [14]3 years ago
4 0

Answer:

0.0642 or 6.42%

Explanation:

The period 't' between the year when the coin was issued, 1794, and 1971 is:

t=1971-1794 \\t=177\ years

If the coin had a value of $5 and after a period of t=177 years it was worth $305,000, the annual tax rate by which the coin appreciated is determined by:

305,000 = 5*(1+r)^{177}\\r=\sqrt[177]{61,000}-1\\r=0.0642=6.42\%

The annual rate was 0.0642 or 6.42%.

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we know that ordinary  annuity:

S= R [(1+i)∧n-1)]/i

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    = 13200 * 5.8765

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a.1)Present value of ordinary annuity:

Formula: Present value = C* [(1-(1+i)∧-n)]/i

                                  =13200 * [(1-(1+.081)∧-5]/.081

                                 =13200 * (1-.6774)/.081

                                =13200 * (.3225/.081)

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a.2)Present value of ordinary Due:

Formula : Present value = C * [(1-(1+i)∧-n)]/i   *  (1+i)

                                    =  13200 * [(1- (1+.081)∧-5)/.081   * (1+.081)

                                 = 13200  * 3.9822 *  1.081

                               =  56822

b-2) Future value=?

we know that:         S= R [(1+i)∧n+1)-1]/i ]  -R

                             = 13200[ [ (1+.081)∧  5+1 ]-1/.081]   - 13200

                           = 13200 (.5957/.081)   -13200

                         = (13200 * 7.3544)-13200

                         = 97078  -  13200

                       =  83878

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