A client has $202,971.39 in an account that earns 8% per year, compounded monthly. The client’s 35th birthday was yesterday and she will retire when the account value is $1 million. At what age can she retire if she puts $250 per month into the account every month, beginning in one month from today?

This is the question. According to a basic hack, I should FV and PMT of same sign and FV and PV of opposite signs! But that doesnt work here!

If i take pv negative, fv and pmt positive, I get a different answer!

If i take pv and pmt positive, i get a different answer!

When using a financial calculator running TVM calculations, you have to set either the PV or FV to negative and have the other as a positive. The cash inflow should be left as positive. It’s not really a ‘basic hack’ just the unfortunate way in which these calculators are designed. Actual TVM calculations using formulae don’t require this.

If you always set the cash inflow to positive, then it’s not merely a matter of setting “either the PV or the FV to negative and . . . the other as . . . positive”. If the PV is an inflow, then it’s positive; if it’s an outflow, then it’s a negative. Similarly for the FV. In short, you have to pay attention to the direction of all cash flows and give them appropriate signs.

It’s not unfortunate at all; it makes perfect sense as the calculations are cash flow calculations so the signs need to represent the directions of the cash flows.