please show all work and do not use excel or a financial calculator. The answer you get must be in the answer key posted at the bottom, thanks!

1. A company has liabilities of $2,000 and $5,000 due at the end of years 1 and 3 respectively. The company can purchase a 1-year $1,000 par value zero-coupon bond with an annual effective yield of 5.6% and a 3-year $1000 par value zero-coupon bond. If the cost of exactly matching the liabilities is $6,068.36, what is the effective yield on the 3-year bond?

Numerical answers (in random order): 6.955, 0.062, 4.5228, 6538.49, 0.04317, 2660.67, 50000, 400.36, 202.1, 3671.29, 1951.62, 4.4621