Tesla wants to raise $70 million to build a new factory. To do this, they issue a bond paying 12% maturing in 18 years. To guarantee that they will be able to repay the principal at maturity, the investors require TSLA to make annual deposits into a sinking fund that pays 5.75% (effective annual rate) that will grow to match the face value at maturity. The current interest rate is 6.75% compounded quarterly.

a) What face value of bonds must TSLA sell to raise their target amount?

b) How much must they deposit each year into the sinking fund?

c) After 9 years how much money is in the sinking fund?

After 9 years, both the current interest rate and the sinking fund rate change by 2%.

d) What is the value of the bonds after this rate change?

e) What should TSLA change their payment to, so that they will still have exactly $70 in the sinking fund when the bond matures?