Today Puzzle #696
Puzzle No. 696 鈥� Friday 13 March
I have foolishly invested £400 in a volatile fund which loses a third of its value after a day, gains a fifth of the original amount the following day & subsequently loses a seventh, gains a ninth, loses an eleventh and so on, always losing and then gaining successively smaller, odd fractions of the original amount. How much will I end up with after a year (to the nearest pound)? You may use a calculator but that involves a tremendous amount of unnecessary effort.
Today’s #PuzzleForToday has been set by Paul Cuddihy of the Royal Hospital School Maths' Department for Pi Day which is on Saturday 14th March.
Click here for the answer
The alternating infinite fraction sum 1-1/3+1/5-1/7+1/9-1/11+1/13……ultimately converges to Pi/4 and therefore the fund is ultimately worth £400 * Pi/4 = £100*Pi = £314.1592……
After one year of successively smaller downs and ups the fund will be worth £314 to the nearest pound.
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