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Financial Mathematics Old FM Forum 

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#53




An investor deposits 1000 at the beginning of each year for five years in a fund earning 5% effective. The interest from this fund can be reinvested at only 4% effective.
Show that the total accumulated value at the end of ten years is 1250(s110:04 − s60:04 − 1) My question is I can find AV(lets call it X) of 5 years = 1000 * [(5 + i/j(s6j 6)] n=5, i=0.05, j =0.04 Is AV of 10 years = X (1+i)^5 or X (1+j)^5? Thanks!
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#54




Quote:
I don't even know where any of these formulas come from, but in many FM problems where there are payments in some string of years but not others, a good strategy (that I think would work here): What is the value if payments (deposits of 1000) are made every year)? Call it Z. Probably a calculation similar to what you did for X, just a different period. What is the value if payments (deposits of 1000) are made only in the years that no payments (deposits) were made? Call it Y. There's a real good chance your number will be what you got for X, because you are evaluating Y at time 10, but it is directly at the end of 5 years of payments/deposits. Then the answer to the question is Z  Y, the value from deposits every year less the value from deposits that were not made. 
#55




Quote:
The formula is in Finan's book for reinvestement: Accumulated Value at the end of the n periods is the sum of the annuity payments and the accumulated value of the interests for annuitydue. AV (t=0 to 10) = s11 3 AV (t=0 to 5) = s6 2 AV = 1250 [(s11  3)  (s6 2)] = 1250[s11  s6  1]
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Last edited by jubair07; 05272019 at 01:14 PM.. 
#56




An investor puts $100 into a mutual fund in the first year and $50 in the second year. At the end of the first year the mutual pays a dividend of $10. The investor sells the holdings in the mutual fund at the end of the second year for $180. Find the dollar weighted return.
100(1+i)^2 + 50(1+i) + 10(1+i) = 180 i = 15.51%. Answer on book is 15.65%. I used simple interest method and i = 15.38%. Where did I go wrong or there another method I didn't apply?
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Last edited by jubair07; 05272019 at 05:50 PM.. 
#57




The $10 dividend should have a negative sign. It is a payment from the fund to you. If i is the effective annual rate you would have 100(1+i)^2  40(1+i) = 180.

#59




An investment manager’s portfolio begins the year with a value of 100,000. Eleven months through the year a withdrawal of 50,000 is made and the value of the portfolio after the withdrawal is 57,000. At the end of the year the value of the portfolio is 60,000. Find the timeweighted yield rate less the dollarweighted yield rate.
I = 60,000+ 50,000  100,000 = 10,000 A=100,000 C=50,000 itid = 0.0956 I checked it*id = 0.0218 = 0.022. But didn't the question ask less and not times? Answer on the book is 0.022. Where did I go wrong?
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Last edited by jubair07; 05272019 at 09:19 PM.. 
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