$1.$ If $$1,000$ is deposited into an account each year earning $10$ percent interest annually for $20$ years, and another $$500$ is deposited into the same account earning $10$ percent interest from years $10$ through $20,$ how much is accumulated into that account at the end of $20$ years?

$2.$ You have just graduated from the Mechanical Engineering program and have found a lucrative job. You plan to retire in $30$ years, but you wish to invest some money for your retirement so in $30$ years your retirement account has accumulated $$500,000.$ For this plan, you decide to pay$10,000$ now and x amount at the end of each month. How much do you have to deposit into that account at the end of each month if the account earns $12\%$ annual interest rate.

$3.$ For problem $2,$ instead of depositing at the end of each month, you decide to pay one lump sum at the end of each year. How much do you have to deposit into the account at the end of each year?

$4.$ An account earns $10\%$ interest annually. $$2,000$ is deposited into that account today, at the end of $5$th year another $2000$ is deposited into the account and additionally monthly deposits of $$300$ is made into that account. How much is accumulated into that account at the end of $10$ years?$5.$ For problem $4,$ no withdrawal is made at the end of ten years but instead, the withdrawal of the funds is made at the end of $20$ years. No additional deposits is made from years $10$ through $20.$How much is accumulated in the account at the end of $20$ years?$6.$ A house is purchased for $$350,000.$ The owner decides to pay $$1800$ per month for the payments. Assuming interest is $3\mathrm{.}25\%$ annually, determine the number of payments for the house to be fully paid$\mathrm{.}7.$ A college fund is set up for $18$ years where $$50$ a month is deposited to it for the duration of that period. Assuming interest rate of $8\%$ annually, how much can be withdrawn from that fund each month from years $19-22\mathrm{.}8.$ Determine the equivalent present worth of the following cash flow diagram $($i$=6\%)\mathrm{.}9.$ Determine the equivalent future worth of the$$20$Kfollowing cash flow diagram $($i$=6\%)\mathrm{.}10.$ Determine the equivalent annual worth of the following cash flow diagram$($i$=6\%).$