Wondering is anyone knows a calculator shortcut for this:
You are building an investment portfolio (balance reducing) to ensure you can maintain purchasing power of $100k a year for 10 years, assuming 3% inflation. The expected return on the portfolio you choose is 2.2%. How much do you need on Day 0?
The answer is $1,013,670. I just don’t know any quicker way to do it than by calculating all 10 periods inflation adjusted payment and discounting by 2.2% then adding them all up
The way I would to it is to use an interest rate of (0.022 - 0.03)/1.03 = -0.0077669 and assume the first payment at time 0 would have been 100,000/1.03 = 97,087.3784. Multiply 97087.3784 by the PV of an immediate annuity for 10 years at -0.779%. Don’t be alarmed by the negative interest rate: that’s just how the math works!
You will get 1,044,079.9337
Then, make it in real terms by discounting by 1.03, so 1,044,079.9337 / 1.03 = 1,013,669.26
The decimals don’t round because I/Y is not calculated with all decimals provided by calculator, so I would set I/Y right after the calculation of (2.2 - 3)/1.03. Remember the calculator uses percentages as numbers, not decimals, so 2.2% is not 0.022, but 2.2.
Using this enhanced accuracy of decimals I get 1,013,669.77, so you can round to 1,013,670
Props to breadmaker for giving light about the correct “interest rate” calculation, I wasn’t getting it right until that.
Thanks to you both, genius. I still dont get why the interest rate isn’t just 2.2%-3% versus 2.2%-3%/1.03 … I’m assuming it’s compounding since I get pretty close the first way
