Question 1131818: The size of the national debt concerns many people, but it continues to grow. Let's look at three possible ways to respond.
1. Pay interest only each year with the principal unchanged.
2. Pay neither principal nor interest so the interest compounds annually. (This is basically the situation in many recent years.)
3. Pay off the principal and interest on a regular basis.
Assume a debt of $10 billion, an interest rate of 6%, and a 30-year period. Look at the total obligation resulting from each of these three strategies. By total obligation, we mean the amount paid plus the amount owed at the end of 30 years.
Which strategy results in the smallest total obligation?
a.) To pay neither the principal nor the interest so the interest compounds annually.
b.) To pay the interest only each year with the principal unchanged.
c.) To pay off the principal and interest on a regular basis.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if you only pay the interest each year, then the total debt at the end of 30 years will be equal to the same as it is today, i.e. 10 billion.
the payments each year will be 6% of 10 billion = .6 billion.
30 * .6 = 18 billion total payments over the 30 year period.
total obligation at the end of the 30 year period = 28 billion.
if you don't do anything but let the interest accrue each year, then the total obligation at the end of the 30 year period will be 10 * 1.06 ^ 30 = 57.43 billion.
if you pay off the principal and interest on a regular basic so that you don't have any debt obligation at the end of the 30 year period, then your payments each year will need to be equal to .72648915 billion for a total of 30 * that = 21.79 billion.
not paying off anything equals 57.43 billion debt at the end of the 30 year period.
just paying off the interest equals 10 billion debt plus 18 billion in payments for a total of 28 billion at the end of the 30 year period.
paying off the principal and interest equals zero debt plus 21.79 billion in payments for a total of 21.79 billion at the end of the 30 year period.
it appears that paying off the principal and the interest provides the least total obligation over the 30 year period when total obligation equals the amount of debt at the end of the 30 year period plus the sum of all payments made over that same 30 year period.
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