PVoa = PMT [(1 - (1 / (1 + i)^n)) / i]
$5,827,420 = 2,000,000[(1 - 1 / (1+i)^4) / i]
5,827,420 / 2,000,000 = [1 - (1 + i)^-4] / i
short of trying to guess i, and then trying to get closer and closer to the correct rate (this process is called iteration), you'd solve it with a financial calculator or spreadsheet...
using my HP12c, I get 14.00004%
PV: 5,827,420
FV: 0
PMT: -2,000,000
n: 4
solve for i: = 14.00004%
notice that I use a negative number for PMT, to show it as an OUTflow - e.g. paying down the principal to a future value of zero. Either the PV OR the payment must be entered as a negative number.
Explain and calculate you get to the website http://rateformoney.com/
At the beginning of 2013, VHF Industries acquired a machine with a fair market value of $5,827,420 by issuing a four-year, noninterest-bearing note in the face amount of $8 million. The note is payable in four annual installments of $2 million at the end of each year.
What is the effective rate of interest implicit in the agreement?
