10,000=106.07{([1 + i/1200]^120 - 1) / [i .(1+i/1200)^120]}, solve for i. Thanks for any help.
This is a TVM formula for either a loan or an annuity of $10,000 that either requires or pays a monthly payment of $106.07 per month for 120 months or 10 years. There is NO DIRECT solution for i in this particular formula. However, computer programs and financial calculators have built into them an iteration and interpolation formulae to arrive at the answer very quickly.
They essentially divide 10,000 / 106.07 =94.277...... So, these built-in formulae "guess" an interest rate that gives an answer slightly above 94.277 and another "guess" that gives an answer that is slighly below 94.277. Then they use interpolation between the three results and rapidly hone in on the actual interest rate that balances the equation.
My own computer has this formula already programmed into it and can very rapidly solve for i once I enter all the known variables into it. Doing that, it immediately comes up with 5% compounded monthly, which is i in this particular problem. And it checks.
