Am I working this out correctly? I need to verify that my code is correct...
$$1000 \cdot \left(\frac{(1 + 0.1 / 12)^{40 * 12} - (1 + 0.06 / 12)^{40 * 12}}{(0.1 / 12) - (0.06 / 12)}\right)$$
Something like this:
53.700663174244 - 10.957453671655 ( = 42.7432095026 )
/
0.0083333333333333 - 0.005 ( = 0.00333333333 )
*
1000
=
12822 962.8636
ps. could someone please help me with the tag selection * blush*
EDIT: Sorry I know this is a mouthful, but if the math don't add up the code can't add up plus I'm actually a designer... not equal to programmer or mathematician. I'm a creative logician :)
Below is part A which must be added (summed) to part B (original question).
A: $$Future Value (FV) of Lumpsum = PV \cdot (1+i/12)^{b*12}$$
B:
$$FV of Growing Annuity = R1 \cdot \left(\frac{(1 + i / 12)^{b * 12} - (1 + g / 12)^{b * 12}}{(i / 12) - (g / 12)}\right)$$
- Current savings for retirement (Rands) = PV
- Rate of return = i/100
- Retirement age (years) – Current age (years) = b
- Current monthly contribution towards retirement (Rands) = R1
- 6/100 (Annual Growth rate of annuities) = g
This is all I have to offer except for the more complicated formula to work out the rest of "Savings for Retirement", but if my example B is correct then the B they gave me is wrong and it's driving me nuts because I'm also having trouble with:
C: $$PV of an Growing Annuity = \left(\frac{R2 \cdot(1 + g / 12)^{b * 12}}{(i / 12) - (g / 12)}\right) \cdot \left(1- \left( \frac{(1 + g / 12)^{b * 12}}{(1 + i / 12)^{n * 12}}\right)\right)$$
- Rate of return = i/100
- Retirement age (years) – Current age (years) = b
- 95 (Assumed age of death) - Retirement age (years) = n
- Monthly income need at retirement (Rands) = R2
- 6/100 (Annual Growth rate of annuities) = g
Which then must be: $$C-(A+B)$$ And finally, let me just give it all...
D: $$FV of Growing Annuity = R3 \cdot \left(\frac{((1 + i / 12)^{b * 12} - (1 + g / 12)^{b * 12} )}{(i / 12) - (g / 12)}\right)$$
- Answer of C-(A + B) = FV of Growing Annuity
- Rate of return = i/100
- Retirement age (years) – Current age (years) = b
- 6/100 (Annual Growth rate of annuities) = g
Answers needed:
- Total Monthly Contribution Needed = R3 (Solve out of D) + R2 (Current Monthly Contributions towards retirement)
- Additional Monthly Contribution Needed = R3 (Solve out of D)
Publishing the calculator now... http://exceed.myib.co.za/calc