If the US government set up a sinking fund to pay off its national debt of approx. $19 trillion dollars, and planned the first payment of $100 billion at the end of the first year. The second and all subsequent payments would increase by 10% per year. At the same time, the national debt would increase by 5% per year. How long would it take the US government to pay off its current national debt of about $19 trillion? Thanks for any help.
This is basically no different than paying off an ordinary loan, with the exception of the fact that the payment increases by 10% per year. As a result, the interest rate on the debt or 5%, will be adjusted accordingly to reflect the 10% increase in payment.
We, therefore, have to adjust the interest rate thus: 1.05/1.10=0.95454... - 1=--0.04545...... The interest rate will be "negative" in this calculation!. Also the first payment will have to be adjusted by the 10% increase, or 100 billion/1.10=90.9090.....etc.
The formula we use is the same common TVM formula used for any loan or mortgage, namely: PMT=PV. R.{[1 + R]^N/ [1 + R]^N - 1}=PMT NEEDED TO PAY OFF A LOAN OF $1
90.9090^9=19^12. -0.04545{[1 + (-.04545)]^N / [1 + (-.04545)]^N - 1]}, by taking the log of both sides and solving for N, we find that:
N=50.55 years for the US government to pay off its entire national debt!!.
