Question $1$

You expect to have $\backslash (\backslash$$ $8,000\backslash )$ in one year. A bank is offering loans at $\backslash (4\mathrm{.}5\backslash \%\backslash )$ interest per year. How much can you borrow today?

Question $2$

Qualcomm has developed a groundbreaking new CPU chip. You expect that the chip's profits to be $\backslash (\backslash$$ $4\backslash )$ million in its first year and that this amount will grow at a rate of $\backslash (5\backslash \%\backslash )$ per year for the next $17$ years. Once the patent expires, Intel will be able to produce the same chip and competition will likely drive profits to zero. What is the present value of the new chip if the interest rate is $\backslash (8\backslash \%\backslash )$ per year?

Question $3$

Assume that Social Security promises you $\backslash (\backslash$$ $50,000\backslash )$ per year starting when you retire $45$ years from today $($the first $\backslash (\backslash$$ $50,000\backslash )$ will get paid $45$ years from now$).$ If the discount rate is $\backslash (4\backslash \%\backslash ),$ compounded annually, and you plan to live for $17$ years after retiring $($so that you will receive a total of $18$ payments including the first one$),$ what is the value today of Social Security's promise?