1. You just graduated from the University of Arizona. Unfortunately, you have also accumulated a $25,000 student loan over four years. Now you need to start paying it off. Suppose the interest rate on the loan is 6% and you need to pay off the loan in 20 years with equal annual payment every year.
a) Figure out what the equal payment amount should be every year. Also figure out a payment schedule of interest and principal payment every year for the 20 years.
b) As we know, the interest on student loan, up to $2,500, is deducted from your gross income to figure out your adjusted gross income (AGI). Suppose your marginal tax rate for the first ten years is 15% and 25% for the next ten years. Please figure out how much this deduction has saved you in federal personal income tax every year for the next twenty years.
c) Please say in a few sentences why federal government should allow you to deduct student loan interest payment from your income to calculate your tax liability.
2.Suppose Pima County issued a $200 million debt to build a new jail in 2005. The interest rate on the bond was 7%. The original debt payment schedule was to pay off the debt in 30 years with equal annual payment every year. After ten years, the interest rate is now down to 5% in 2015. The County wants to refinance its debt at this low rate, that is to say to issue a new debt at 5% to pay off what is left of the old debt and then pay debt service on the new debt. If the city can issue a new debt at 5% with a maturity of 20 years beginning in 2015, please figure out:
a) What is the annual level payment on the old debt?
b) What is the amount of the new debt?
c) What is the saving in annual payment every year for the next 20 years? (Assume also an equal annual payment on the new debt.)
d) Use this case as an example, briefly comment on why citizens should care about your local government debt management.
3. Say Pima County now has an annual budget of $100 million, and by county finance rule, it cannot spend more than 10% of its budget on debt service, including both principal and interest payment. Suppose the county wants to take out a 20-year loan for a capital project. It will be paid back with 20 annual equal payments.
a) If the current interest rate is 5% for a 20-year loan, what is the maximum amount the county can borrow for the project?
b) Suppose the current interest rate now has dropped to 3%, how much more can the county borrow, so that it can fund other county capital projects?
c) Please use this example to explain why the Federal Reserve wants to keep long-term interest rate low in light of our current weak economic condition.