$7.$ You have just deposited X dollars in your bank account that pays interest of $9$ percent p$.$a$.$ You discover that at the end of one year you have $ $17,545$ in the account. What was X$,$ that is$,$ the amount of money that you deposited today? $($Record your answer without a dollar sign, without commas and round your answer to $2$ decimal places; that is$,$ record $$3,245\mathrm{.}847$ as $3245\mathrm{.}85).$

$8.$ You want to withdraw $ $34,156$ from your account at the end of one year and $ $20,795$ at the end of the second year. How much should you deposit in your account today so that you can make these withdrawals? Your account pays $8$ percent p$.$a$.($Record your answer without a dollar sign, without commas and round your answer to $2$ decimal places; that is$,$ record $$3,245\mathrm{.}847$ as $3245\mathrm{.}85).$

$9.$ You deposit $ $7,147$ in your account today. You make another deposit at t $=1$ of $ $6,705.$ How much will there be in your account at the end of year $1$ if the interest rate is $7\mathrm{.}9$ percent p$.$a$.?($Record your answer without a dollar sign, without commas and round your answer to $2$ decimal places; that is$,$ record $$3,245\mathrm{.}847$ as $3245\mathrm{.}85).$

$10.$ You deposit $ $74,854$ in your account today. You make another deposit at t $=1$ of $ $74,911.$ How much will there be in your account at the end of year $2$ if the interest rate is $18$ percent p$.$a$.?($Record your answer without a dollar sign, without commas and round your answer to $2$ decimal places; that is$,$ record $$3,245\mathrm{.}847$ as $3245\mathrm{.}85).$

$11.$Your account pays interest at $8$ percent p$.$a$..$ You deposit $ $31,855$ in it today. You must have exactly $ $83,875$ in the account at the end of two years. What should you do at the end of the first year $($that is$,$ what dollar amount must you deposit$)$ to ensure this? $($Record your answer without a dollar sign, without commas and round your answer to $2$ decimal places; that is$,$ record $$3,245\mathrm{.}847$ as $3245\mathrm{.}85).$

$12.$ You invest $ $4,417$ in an account today. You make no additional deposits into the account. One year from today there is $ $5,418$ in the account. What is the nominal interest rate that you earned on your money? $($Record your answer as a percent rounded to $1$ decimal place; for example, record $\mathrm{.}527945=52\mathrm{.}8\%$ as $52\mathrm{.}8).$

$13.$ You invest $ $4,417$ in an account today. You make no additional deposits into the account. One year from today there is $ $5,418$ in the account. What is the nominal interest rate that you earned on your money? $($Record your answer as a percent rounded to $1$ decimal place; for example, record $\mathrm{.}527945=52\mathrm{.}8\%$ as $52\mathrm{.}8).$

$14.$ Assume Sheryl Jenkins wants to accumulate $ $12,121\mathrm{.}12$ in two years. She currently has $ $10,860\mathrm{.}67$ to invest. What interest rate must she earn on her investment $($that is$,$ if she deposits $ $10,860\mathrm{.}67$ today$)$ to have $ $12,121\mathrm{.}12$ exactly two years from today?$($Record your answer as a percent rounded to $1$ decimal place; for example, record $\mathrm{.}527945=52\mathrm{.}8\%$ as $52\mathrm{.}8).$

$15.$ Assume Jed Gerbil invested $ $14,567$ into an account exactly two years ago. The account has an interest rate of $10\mathrm{.}9\%$ p$.$a$.$ How much does Jed have in his account today $($that is$,$ exactly two years after the initial deposit$)?($Round your answer to the nearest cent and record your answer without a dollar sign and without commas. For example, record $$1,356\mathrm{.}8382$ as $1356\mathrm{.}84).$