Mathematical Interest Theory. Economics/Mathematics Quesiton. 

1. A 5 year bond has a face value $30,000 and semi-annual coupons of $650. The bond is purchased to achieve a return of i^(2)=0.046.

a. Find the purchase price.

b. Divide rhe 4th coupon into interest and premium adjustment.

c. What is the bond's value (to the purchaser) immediately after the 4th coupon is received?

d. What is the bond's value three months after the 4th coupon is paid?

2a. The bond is sold immediately after the 4th coupon payment to an investor who buys it to achieve a return of 0.024 per six months. Find the price

b. Suppose insted the new investor buys the bond halfway between the 4th and 5th coupon payments. Calculate this price.

3. A bank lan of $500,000 at an interest rate of 0.07 is to be reapid in 8 years. The borrower must pay the annual interest directly to the bank and must make annual deposits into a sinking fund of an amount that will accumulate to the loan amount in 8 years. The sinking fund earns interest at a rate of 0.03.

a. Find the sinking fund payment.

b. Find the borrower's annual effective interest rate.