pv = pmt * (1 - (1/(1+r)^n)/r
when pmt = 450 and r = .06/12 and n = 5*12, the formula becomes:
pv = 450 * (1 - (1/(1+.06/12)^(5*12)))/(.06/12) = 23,276.50 rounded to 2 decimal places.
i confirmed this is correct by using a financial calculator to get the same results.
the time periods involved are assumed to be months.
the interest rate per year is divided by 12 to get the interest rate per month.
the number of years is multiplied by 5 to get the number of months.
be careful of the parentheses.
they have to be there in the correct order and number.
to simplify the calculations, you can provide some of the calculations up front.
this is especially useful if you have multiple memory locations to store them in.
if not, then you can truncate the number of decimal places to 6 and should be able to get the same answer when rounded to 2 decimal places.
here's the same problem with the intermediate calculations truncated to 6 decimal places, if required.
.06/12 = .005
5*12 = 60
the formula becomes:
p = 450 * (1-(1/(1+.005)^60))/.005 = 23,276.50 rounded to 2 decimal places.
the biggest problem is making sure you got the parentheses right.
your go to alternative is to use a financial calculator, if you're allowed to use them.
a financial calculator that i use online can be found at:
https://arachnoid.com/finance/index.html
inputs to this calculator would be:
fv = 0
np = 5 years * 12 months per year = 60
pmt = -450
ir = 6% / 12 = .5 (calculator uses percent, not rate)
payments are made at the end of each time period.
press pv and the calculator tells you that the present value is equal to 23,276.50.
you get the same answer with a lot less worry about whether you entered the problem correctly into your calculator.
even if you can't use a financial calculator, it's a good way to check whether you got the right answer or not.
here's a display of what the calculator looks like with your inputs and the result.
pmt was entered as negative because it's money going out.
pv was shown as positive because it's money coming in.