$1.$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.

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$.$

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.

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