Questions   
Sort: 
 #10
avatar+1038 
+5

The following data sets shows first 12 months and the last 12 months of a hypothetical account of 360 interest cycles.

 

The first column displays the $200 deposit; the second column displays the end of month interest payment on the previous balance and the $200 first day of month deposit.

Column 3 displays the new balance.

Column 4 is the multiplier that weights the deposit for the purpose of interest calculation. The multiplier is from 1 to 0, representing the average daily deposit of the $200, where 1 is a deposit on the first day and 0 is a deposit on the last day. (No withdraws are made from this account and only the deposit is weighted).

Column 5 is the average daily of the deposit.

Column 6 is the interest.

Column 7 is the balance.

 

Note that the final balance in column 3 matches the annuity due, while the final balance in column 7 matches the annuity ordinary.

 

 

$$\displaystyle

\noindent \small {First data set. Months 1-12}\\

\begin{tabular}{lllllll}
1 & 2 & 3 & 4 & 5 & 6 & 7 \\
\hline

200.00 & 0.50 & 200.50 & 0.00 & 0.00 & 0.00 & 200.00 \\
200.00 & 1.00 & 401.50 & 0.00 & 0.00 & 0.50 & 400.50 \\
200.00 & 1.50 & 603.01 & 0.00 & 0.00 & 1.00 & 601.50 \\
200.00 & 2.01 & 805.01 & 0.00 & 0.00 & 1.50 & 803.01 \\
200.00 & 2.51 & 1,007.53 & 0.00 & 0.00 & 2.01 & 1,005.01 \\
200.00 & 3.02 & 1,210.54 & 0.00 & 0.00 & 2.51 & 1,207.53 \\
200.00 & 3.53 & 1,414.07 & 0.00 & 0.00 & 3.02 & 1,410.54 \\
200.00 & 4.04 & 1,618.11 & 0.00 & 0.00 & 3.53 & 1,614.07 \\
200.00 & 4.55 & 1,822.65 & 0.00 & 0.00 & 4.04 & 1,818.11 \\
200.00 & 5.06 & 2,027.71 & 0.00 & 0.00 & 4.55 & 2,022.65 \\
200.00 & 5.57 & 2,233.28 & 0.00 & 0.00 & 5.06 & 2,227.71 \\
200.00 & 6.08 & 2,439.36 & 0.00 & 0.00 & 5.57 & 2,433.28
\end{tabular}$$

 

$$\displaystyle

\noindent \small {First data set. Months 349-360}\\

\begin{tabular}{lllllll}
1 & 2 & 3 & 4 & 5 & 6 & 7 \\
\hline
200.00 & 278.06 & 111500.59 & 0.00 & 0.00 & 276.86 & 111222.53 \\
200.00 & 279.25 & 111979.84 & 0.00 & 0.00 & 278.06 & 111700.59 \\
200.00 & 280.45 & 112460.29 & 0.00 & 0.00 & 279.25 & 112179.84 \\
200.00 & 281.65 & 112941.94 & 0.00 & 0.00 & 280.45 & 112660.29 \\
200.00 & 282.85 & 113424.79 & 0.00 & 0.00 & 281.65 & 113141.94 \\
200.00 & 284.06 & 113908.85 & 0.00 & 0.00 & 282.85 & 113624.79 \\
200.00 & 285.27 & 114394.13 & 0.00 & 0.00 & 284.06 & 114108.85 \\
200.00 & 286.49 & 114880.61 & 0.00 & 0.00 & 285.27 & 114594.13 \\
200.00 & 287.70 & 115368.31 & 0.00 & 0.00 & 286.49 & 115080.61 \\
200.00 & 288.92 & 115857.23 & 0.00 & 0.00 & 287.70 & 115568.31 \\
200.00 & 290.14 & 116347.38 & 0.00 & 0.00 & 288.92 & 116057.23 \\
200.00 & 291.37 & 116838.75 & 0.00 & 0.00 & 290.14 & 116547.38
\end{tabular}$$

 

The second data sets are the same as the first, except the multiplier is set to 0.75. This corresponds to a depositor making two deposits of $100 each on the first and 15 of each 30-day month.

 

$$\displaystyle

\noindent \small {Sceond data set. Months 1-12}\\

\begin{tabular}{lllllll}
1 & 2 & 3 & 4 & 5 & 6 & 7 \\
\hline
200.00 & 0.50 & 200.50 & 0.75 & 150.00 & 0.38 & 200.38 \\
200.00 & 1.00 & 401.50 & 0.75 & 150.00 & 0.88 & 401.25 \\
200.00 & 1.50 & 603.01 & 0.75 & 150.00 & 1.38 & 602.63 \\
200.00 & 2.01 & 805.01 & 0.75 & 150.00 & 1.88 & 804.51 \\
200.00 & 2.51 & 1007.53 & 0.75 & 150.00 & 2.39 & 1006.90 \\
200.00 & 3.02 & 1210.54 & 0.75 & 150.00 & 2.89 & 1209.79 \\
200.00 & 3.53 & 1414.07 & 0.75 & 150.00 & 3.40 & 1413.19 \\
200.00 & 4.04 & 1618.11 & 0.75 & 150.00 & 3.91 & 1617.10 \\
200.00 & 4.55 & 1822.65 & 0.75 & 150.00 & 4.42 & 1821.51 \\
200.00 & 5.06 & 2027.71 & 0.75 & 150.00 & 4.93 & 2026.44 \\
200.00 & 5.57 & 2233.28 & 0.75 & 150.00 & 5.44 & 2231.88 \\
200.00 & 6.08 & 2439.36 & 0.75 & 150.00 & 5.95 & 2437.84
\end{tabular}$$

 

$$\displaystyle

\noindent \small {Sceond data set. Months 349-360}\\

\begin{tabular}{lllllll}
1 & 2 & 3 & 4 & 5 & 6 & 7 \\
\hline
200.00 & 278.06 & 111500.59 & 0.75 & 150.00 & 277.76 & 111431.07 \\
200.00 & 279.25 & 111979.84 & 0.75 & 150.00 & 278.95 & 111910.02 \\
200.00 & 280.45 & 112460.29 & 0.75 & 150.00 & 280.15 & 112390.17 \\
200.00 & 281.65 & 112941.94 & 0.75 & 150.00 & 281.35 & 112871.52 \\
200.00 & 282.85 & 113424.79 & 0.75 & 150.00 & 282.55 & 113354.08 \\
200.00 & 284.06 & 113908.85 & 0.75 & 150.00 & 283.76 & 113837.84 \\
200.00 & 285.27 & 114394.13 & 0.75 & 150.00 & 284.97 & 114322.81 \\
200.00 & 286.49 & 114880.61 & 0.75 & 150.00 & 286.18 & 114808.99 \\
200.00 & 287.70 & 115368.31 & 0.75 & 150.00 & 287.40 & 115296.39 \\
200.00 & 288.92 & 115857.23 & 0.75 & 150.00 & 288.62 & 115785.00 \\
200.00 & 290.14 & 116347.38 & 0.75 & 150.00 & 289.84 & 116274.84 \\
200.00 & 291.37 & 116838.75 & 0.75 & 150.00 & 291.06 & 116765.90
\end{tabular}$$

 

...

Aug 2, 2015
Aug 1, 2015
 #12
avatar+2973 
0

Alright, lets attack already before the admins interrupt the server for a maintenance 

*pays the 1,000 gold required to attack

*barrages sydneys boom cannons and shock launchers

*uses artilery to set off boom mines and mines 

*deploys landing craft of riflemen and places flare spell at the machine guns

*deploys 2 more landing crafts, holding heavys and zookas to back up the riflemen

*drops a shock bomb at the rocket launchers

*deploys 3 more landing crafts, this time containing Medics, Grenaiders, and Tanks

*grenadiers attack the flamethrowers, and prototype sydney weapons, while being backed up by the tanks

*Australlian Military comes and does a desperate attempt to stop the Royal Military

*Australlian army is a lot more advanced though, taking out my tanks and medics right away

alright, time to deploy a new spell, mwahaha

*deploys the tsunami weather spell, starts a tsunami that destroys much of sydney, qlthough working, is also k*****g my zookas and heavys

*deploys smoke screen spell at my remaining troops

alright, army is way too advanced

time for EVERYTHING to burn!

*deploys last few landing crafts of mass-scorchers and deploys critters 

*scorchers and critters begin igniting many buildings, advance to the Castle

*deploys anomaly hog riders and royal heroes to attack the castle 

*castle gets destroyed, Australlian army retreats rather than surrender, hides underground

haha, australlia. And the whole wide world is ours!

*operation australi-doom over, operation was a success

*we spot melody, appearing as a young woman who looked like she just got out of adolescence, carrying a rifle and tried attacking, but the royal heroes caught her

melody, for now on Australlia is under Royal Control! You have 2 choices: 1: stay out of this and enjoy royal luxury or 2: protest and prepare to be executed. Which one will it be?

Aug 1, 2015
 #4
avatar+26 
0
Aug 1, 2015
 #11
avatar+2973 
0

Operation Africa: Success

I wouldnt say that melody, 

*after hours of scouting the map of sydney

Me:Professor, lets make another prototype. Theyre strong in numbers

professor: im afraid we cannot, however, we can make a new line up of Troops! We shall no longer experiment with Clash Of Clans troops, its time we go to Boom Beach.

me: alright

*after many hours of experimenting with boom beach

me: yes! Our Boom Beach Army is finally complete! Sydney, say hello to:

RifleMen (carry rifle, strong in numbers)

Heavys (carry mini machine gun, used as a take a hit troop)

Zookas (carry bazookas to shoot and cause much damage to buildings in a long range)

Warriors (carrys a Thor's hammer, which heals the warrior with every swing, causes much damage)

Tanks 2.0 (similar to the zooka, but more damage and way more health)

Medics 2.0 (ones that run in the battle field and does splash heal within a radius)

now that, were just getting started

we have 2 of the most op troops in the game:

Grenadier (shoots gernades that do splash damage, but inaccurate)

now, for the star of the show:

Scorcher (3.0 version of the tank, no driver, and all it does is BURN EVERYTHING. EVERYTHING MUST BURN!, just like in closing stores they say everything must go)

now lets bring some new spells and artilery...from a GUNBOAT!!

Artillery (does major damage in accurate range, only one shot per placement)

Flare Spell (guides troops to where you want them to go, especially when attacking an unnecessary building)

Heal Spell 2.0 aka the MedKit (does more healing, but in less time)

Shock Bomb (shocks anything within its radius, like the Shock Launcher but for offense)

Barrage (shoots multiple artilery, like the grenadier, does splash damage, but inaccurate)

Smoke Screen Spell (smokes my troops so your defenses melody cant see them, but troops cannot fire or be fired)

Last but not least:

Critters! (Robotic troops that can do some real damage and have decent health, however they cannot follow the flare spell or be healed by the medkit to balance the game)

aleight, since Sydney is located in the ocean, we will launch the attack

get ready to be Royaled, Australi-DOOM!

Aug 1, 2015
 #93
avatar+118723 
0

 @@ End of Day Wrap   Sat 1/8/15     Sydney, Australia Time   10:42pm  ♪ ♫

 

Hi all,

It was quite but it always amazes me how busy I am on a quiet day 

Anyway there were some great answers from CPhill, Alan and EinsteinJr.  Thank you.  I hope I didn't miss anyone.

 

If you would like to comment on other site issues please do so on the Lantern Thread.  Thank you.    

 

Interest Posts:

 

1)  Octogonal problem                              Thanks CPhill

2)  Solving a fractional inequality               Melody.

3)  Given Cos, find tan                               Thanks Alan

                                

                       ♫♪  ♪ ♫                                ♬ ♬ MELODY ♬ ♬                                 ♫♪ 

Aug 1, 2015
 #1
avatar+118723 
0
Aug 1, 2015
 #4
avatar+118723 
+1
Aug 1, 2015

0 Online Users