Answer to Question #141498 in Economics of Enterprise for Jayden cruz

Question

Find the annual payments to extinguish a debt of P10,000.00 payable for 5years at 12% interest *

Answer 1

$\bold {Answer}$

Annual Payment, $PMT = \$2,774.10$

$\bold {Solution}$

Assuming the annual payments are made at the end of each year, the question represents an ordinary annuity.

We are a given:

$PV = \$10,000$

$i\% = 12\% \space p.a$

$n = 12 \space years$

The question requires the value of yearly future payments required to clear the $10,000 present debt at 12% annual interest.

For an ordinary annuity,

$PV = PMT \left[\dfrac {1-(1+r)^{-n}}{r} \right]$

$10,000= PMT \left[\dfrac {1-(1+0.12)^{-5}}{0.12} \right]$

$10,000 = PMT \left[\dfrac {1-1.12^{-5}}{0.12} \right]$

$=> PMT = \dfrac {10,000×0.12}{1-1.12^{-5}}$

$= \dfrac {1,200}{0.4325731442}$

$= \$2,774.0973199$

$= \bold {\$2,774.10} \space per \space year$