Answer to Question #127418 in Financial Math for Prathap

Question

Starting on 2011, and continuing until 2022, a company will repay a debt with payments of Rs. 250 000 annually. What equal annual deposits in a fund paying 5% annually beginning on 2001, and continuing until 2022, are required to repay the debt?

Answer 1

The total debt from 2011-2022 will amount to:

$250,000\times 12= 3,000,000$

Using the future value formulas, the deposit is computed as follows:

The present value of an annuity due will be composed as follows:

$\text{Present value of an annuity due}=\text{Annuity}\times \dfrac{1-(1+r)^{-n}}{r}\times (1+r)$

$3,000,000=\text{Annuity}\times \dfrac{1-(1+0.05)^{-22}}{0.05}\times (1+0.05)$

Therefore, the annuity will be equivalent to:

$\text{Annuity}=\dfrac{3,000,000}{13.82115271}=217,058.6$