Answer: Since Frank made his most recent EMI payment today, Frank needs 76,136.52 in order to pay off his mortgage today.
We follow these steps to arrive at the answer:
We first calculate the EMI on loan taken out:
The EMI is nothing but P (constant amount paid or received periodically) in the Present Value of an Annuity formula. The formula is
[tex]\mathbf{PV_{Annuity} = EMI* \left[ \frac{1 - (1+r)^{-n}}{r} \right]}[/tex]
Substituting the values from the question we get,
150000 = EMI* \left[ \frac{1 - (1+\frac{0.05}{12})^{-(25*12)}}{\frac{0.05}{12}} \right]
Solving we get,
[tex]150000 = EMI* \left[\171.06\right][/tex]
[tex]\frac{150000}{171.060047} = EMI[/tex]
[tex]\mathbf{EMI = 876.8850623}[/tex]
We then construct the Amortization table attached below. At the end of 16 years or 192 periods ([tex]16*12[/tex]), we can see that the principal outstanding is $76,136.52.
