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?
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"
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