4 of 5 (0 complete) This Test: 100 pts possible Twenty years ago John in ested $

Question

4 of 5 (0 complete) This Test: 100 pts possible Twenty years ago John in ested $10,000 in a mutual fund. The value of is investment declined by 17% during the first year and then dedi ed anot 30% during the second year. Eighteen more years have passed, and John's cumulative retum over the 20-year period is a 507% r Click the icon to view the interest and annuity table for discrete compounding when i#7% per year. a. What is the value of the original investment now? The value of the original investment now is (Round to the nearest dollar.) b. If inflation has averaged 7% per year over the past 20 years, what is the spending power equivalent of the answer to Part (a) in terms of real dollars 20 years ago? The spending power equivalent in terms of real dollars 20 years ago is S (Round to the nearest dollar.) c, what is the real compound interest rate earned over the The real compound interest rate is-%. (Round to two decimal places.) 20-year period? the past 18 years. what compound annual rate of returm (yield) was earmed on John's nvestment? The compound annual rate of return is % (Round to two decimal places.) Enter your answer in each of the answer boxes.

Explanation / Answer

A) Value of original investment now is 10,000*507%

=50700$

B) This can be found using formula of Present value

PV = FV/(1+r)^n

=50700/(1.07)^20

=50700/3.869684

=13101.84$

C) Real compound interest can be found as follows

FV=PV(1+r)^n

=50700 = 10000(1+r)^20

=5.07 = (1+r)^20

Assuming r = 8.46%

(1.0846)^20 = 5.07

Hence real compound interest is of 8.46%

D) During first year investment fell by 17%, hence value of investment at end of year = 8300$

During second year investment fell by 30%, hence value of investment at end of year 2 = 8300*0.7 = 5810$

Now return earned over 18 years can be calculated as follows

FV=PV(1+r)^n

=50700 = 5810(1+r)^18

=8.726 = (1+r)^18

Assuming r to be 12.79%

(1.1279)^18 = 8.72

Thus compound annual rate = 12.79%

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