A debt of $2; 000 is due at the end of 5 years (t = 5). It is proposed that X do

Question

A debt of $2; 000 is due at the end of 5 years (t = 5). It is proposed that X dollars be paid now (t = 0), and with another X dollars be paid in 10 years' time (t = 10) to completely pay off the debt. We want to determine the value of X if the eective annual interest rate for the rst four years (t = 0 to t = 4) is 8%, for the next four years (t = 4 to t = 8) is 5%, and for the last two years (t = 8 to t = 10) is 6%. Give any equation required for calculation of X and specify the value of all parameters in the equations. Numerical answer not needed.

A debt of $2,000 is due at the end of 5 years (1-5). It is proposed that X dollars be paid now (t = 0), and with another X dollars be paid in 10 years. time ( 10) to completely pay off the debt. We want to determine the value of X if the effective annual interest rate for the first four years (t = 0 to t = 4) is 8%, for the next four years (t = 4 to t = 8) is 5% and for the last two years (t = 8 to 10) is 6%. Give any equation required for calculation of X and specify the value of all parameters in the equations. Numerical answer not needed.

Explanation / Answer

Prsent Value of debt=2000/(1.08^4*1.05)

Present value of payments=X+X/(1.08^4*1.05^4*1.06^2)

Present value of debt=Present value of payments

=>2000/(1.08^4*1.05)=X+X/(1.08^4*1.05^4*1.06^2)

=>X+X/(1.08^4*1.05^4*1.06^2)-2000/(1.08^4*1.05)=0

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