$1.$Determine the future value according to the following situation: John's salary was increased last week and he is considering investing or saving it instead of spending it$.$ He went to a branch of the State Bank and they offered him two alternatives. First they offered him a certificate of deposit that pays a semiannual interest rate of $2\mathrm{.}5\%$ with a maturity period of $5$ years. You also have the opportunity to deposit into a savings account that pays a monthly interest rate of $1\mathrm{.}9\%.$ Assuming John has $$10,000$ available, determine which of the two options will have a greater future value at the end of $5$ years.

$2.$ Determine the present value: Jenny was presented with an investment opportunity that promises to pay her $$2,500$ at the end of $10$ years. The condition to be paid this amount of money is that you have to deposit $$1,500$ today and wait for that period of time. The prevailing discount rate at the time of this offer is $2\mathrm{.}90\%$ discounted quarterly. Determine the present value and describe to Jenny whether this investment opportunity is worth it$.$

$3.$ Determine the years it will take using the following information: $($a$)$ $$500$ increasing to $$4,311\mathrm{.}55$ if invested at an interest rate of $9\%$ compounded annually; $($b$)$ $$100$ decreasing by $$2\mathrm{.}07$ if invested at $9\%$ compounded annually.

$4.$ Determine the interest rate using the following information: $($a$)$ $$500$ increasing to $$2,408\mathrm{.}95$ in $12$ years; $($b$)$ $$300$ decreasing to $$199\mathrm{.}53$ if invested in $7$ years