a bank makes a package of three loans to a small business. $($a$)$ $$120000$ amortized monthly for ten years at a nominal discount rate of $6\mathrm{.}8\%$ convertible monthly. $($b$)$ $$100000$ to be repaid by monthly sinking fund payments for ten years where interest is assessed at a rate of $5\mathrm{.}4\%$ nominal convertible monthly and the sinking fund earns $4\%$ nominal interest convertible monthly. the bank receives the sinking fund deposits. $($c$)$ $$200000$ to be repaid with interest at the end of ten years with an effective rate of discount of $8\mathrm{.}2\%$ throughout the ten years. find the bank's annual effective yield on each of these loans individually and on the package of loans over the ten$-$year period.