Math help

[xrapidx]

My brain is fried today.

Can someone assist me with a calculation? I'm trying to prove something to the bank with regards to an investment (RA).

If I save R200 every month for the next 35 years, at a return of 10%/pa, and an increase of 10%/pa to the R200, how much will I have at the end of 35 years?

I want to show them that R200 is actually quite a lot per month.

 

[Morgoth]

I got to R 7237.47
after 35 years.

 

[killadoob]

rapid can this be influenced by the economy? If so they could end up with nothing after 35 years .

 

[xrapidx]

Thats a fail

R200 x 12 x 35 is already : R84,000... Remember its R200 per month, that earns 10% interest per year... and also grows by 10% each year... so the first year would be R200/pm, second year R220/pm, third year R242.00/pm, etc.

I'm reckoning millions

 

[xrapidx]

rapid can this be influenced by the economy? If so they could end up with nothing after 35 years .

No - I made it easy with 10% - I'm using the increase of 10% per month as inflation

 

[Morgoth]

my bad I took it as 35 per year
this means you will have R104632.76? after 35 years if interest is 10% per year.

 

[xrapidx]

my bad I took it as 35 per year
this means you will have R104632.76? after 35 years if interest is 10% per year.

Thats not millions - I want millions!

What calculation did you use ?

 

[xrapidx]

I get this, without the 10% increase per year.

Year Year Deposits Total Deposits Year Interest Total Interest Total Sum
1 2,400.00 2,400.00 134.06 134.06 2,534.06
2 2,400.00 4,800.00 399.41 533.46 5,333.46
3 2,400.00 7,200.00 692.54 1,226.00 8,426.00
4 2,400.00 9,600.00 1,016.37 2,242.37 11,842.37
5 2,400.00 12,000.00 1,374.11 3,616.48 15,616.48
6 2,400.00 14,400.00 1,769.31 5,385.78 19,785.78
7 2,400.00 16,800.00 2,205.89 7,591.67 24,391.67
8 2,400.00 19,200.00 2,688.18 10,279.85 29,479.85
9 2,400.00 21,600.00 3,220.98 13,500.83 35,100.83
10 2,400.00 24,000.00 3,809.57 17,310.40 41,310.40
11 2,400.00 26,400.00 4,459.80 21,770.20 48,170.20
12 2,400.00 28,800.00 5,178.11 26,948.31 55,748.31
13 2,400.00 31,200.00 5,971.63 32,919.94 64,119.94
14 2,400.00 33,600.00 6,848.25 39,768.19 73,368.19
15 2,400.00 36,000.00 7,816.66 47,584.85 83,584.85
16 2,400.00 38,400.00 8,886.48 56,471.34 94,871.34
17 2,400.00 40,800.00 10,068.32 66,539.66 107,339.66
18 2,400.00 43,200.00 11,373.92 77,913.58 121,113.58
19 2,400.00 45,600.00 12,816.23 90,729.81 136,329.81
20 2,400.00 48,000.00 14,409.57 105,139.38 153,139.38
21 2,400.00 50,400.00 16,169.75 121,309.13 171,709.13
22 2,400.00 52,800.00 18,114.25 139,423.38 192,223.38
23 2,400.00 55,200.00 20,262.36 159,685.73 214,885.73
24 2,400.00 57,600.00 22,635.40 182,321.14 239,921.14
25 2,400.00 60,000.00 25,256.93 207,578.07 267,578.07
26 2,400.00 62,400.00 28,152.98 235,731.05 298,131.05
27 2,400.00 64,800.00 31,352.27 267,083.32 331,883.32
28 2,400.00 67,200.00 34,886.58 301,969.90 369,169.90
29 2,400.00 69,600.00 38,790.97 340,760.86 410,360.86
30 2,400.00 72,000.00 43,104.20 383,865.06 455,865.06
31 2,400.00 74,400.00 47,869.09 431,734.15 506,134.15
32 2,400.00 76,800.00 53,132.92 484,867.07 561,667.07
33 2,400.00 79,200.00 58,947.94 543,815.00 623,015.00
34 2,400.00 81,600.00 65,371.87 609,186.87 690,786.87
35 2,400.00 84,000.00 72,468.47 681,655.34 765,655.34

 

[Morgoth]

PV = FV — r·PV = FV/(1+r).

I think mine is on the R200 only, heh I cant remember the one for increase in investment probably have to set my PV to 200(1+20%)^35 so its higher then that total.

 

[xrapidx]

I keep getting different results, with a 10% increase per annum - the monthly payment in year 35 will be R 5,109.53 - meaning the total balance will be R 2,146,004.27 in fee's.

 

[AirWolf]

I worked it out in Excel using monthly compounding. It comes to R655879 after 35 years @ 10% interest p.a and 10% payment escalation a year.

 

[Morgoth]

I worked it out in Excel using monthly compounding. It comes to R655879 after 35 years @ 10% interest p.a and 10% payment escalation a year.

its investment per month.

 

[AirWolf]

its investment per month.

Yes starting with R200 a month.

If you start the same process with R304.94 starting value per month, you'll get R1000019 after 35 years.

 

[xrapidx]

Yes starting with R200 a month.

If you start the same process with R304.94 starting value per month, you'll get R1000019 after 35 years.

Calculation if you have it please

 

[bemark]

I get R 2,242,670.42 after the 35 years. But normalising it to today's monetary value using inflation of 10% pa gives the figure R 79,803.41

Equations

Total: (Initial payment pm)*(interest pa)^(no. of payment increases over whole period)*(interest pa)/(interest pm - 1)*(years in period) =
(200)*(1.1)^(34)*(0.1)/(nroot(1.1;12)-1 [=0.0080])*(35)

Total normalised: (Total over period) / (inflation pa+1)^(years) =
(R 2,242,670.42) / (1.1^35)

 

[The_Pumpkin_King]

HP 10bII FTW!

 

[phiber]

What benmark has done seems right... just do it in excel, its simple math

 

[xrapidx]

I get R 2,242,670.42 after the 35 years. But normalising it to today's monetary value using inflation of 10% pa gives the figure R 79,803.41

Equations

Total: (Initial payment pm)*(interest pa)^(no. of payment increases over whole period)*(interest pa)/(interest pm - 1)*(years in period) =
(200)*(1.1)^(34)*(0.1)/(nroot(1.1;12)-1 [=0.0080])*(35)

Total normalised: (Total over period) / (inflation pa+1)^(years) =
(R 2,242,670.42) / (1.1^35)

Thanks man - perfectly useful first post.

 

[AirWolf]

I worked it out in Excel using monthly compounding. It comes to R655879 after 35 years @ 10% interest p.a and 10% payment escalation a year.

My bad, the above is incorrect. I've adjusted the spreadsheet and come to R2,438,967.92

I get R 2,242,670.42 after the 35 years. But normalising it to today's monetary value using inflation of 10% pa gives the figure R 79,803.41

Equations

Total: (Initial payment pm)*(interest pa)^(no. of payment increases over whole period)*(interest pa)/(interest pm - 1)*(years in period) =
(200)*(1.1)^(34)*(0.1)/(nroot(1.1;12)-1 [=0.0080])*(35)

Total normalised: (Total over period) / (inflation pa+1)^(years) =
(R 2,242,670.42) / (1.1^35)

Thanks for the info. But without more brackets, I can't seem to figure out what is in the numerator, denominator and power.

 

[bemark]

@xrapidx: No problem, glad to have helped.

@AirWolf: Fair point. With added brackets (and a bit of refining of the "interest pm" and "interest pa" parts - the values and result stays the same though) it comes to

Total: (Initial payment pm)*((interest pa+1)^(no. of payment increases over whole period))*(years in period)*((interest pa)/(interest pm)) =
(R 200)*((1.1)^(34))*(35)*((0.1)/(nroot(1.1;12)-1 [=0.0080]))