$7)$ You deposit some money in a savings account offering an annual percentage rate of $7\%,$

compounded monthly. What is the effective annual rate $($EAR$)$ that your investment will

earn? $(12\mathrm{.}5$ points$)$

$8)$ You are offered an investment that will pay you $($and your heirs$)20,000$ income per

year forever, beginning one year from now. Assuming an annual risk$-$free interest rate of

$8\%,$ what would you expect to pay for this offer? Round your answer to the nearest euro.

$(10$ points$)$

$9)$ To buy a house, John takes out a fixed$-$rate amortizing mortgage of $$110,000$ for $20$

years, with an annual percentage rate $($APR$)$ of $11\mathrm{.}3\%,$ compounded monthly. What will

be John's required monthly payment? $($Each payment includes principal and interest $(15$

points$)$

$10)$ You and a group of friends are planning to donate money to fund a community sporting

event every year indefinitely, beginning one year from now. Assume the event costs

$6,700$ in the first year, and this amount will increase each year by $4\mathrm{.}2\%.$ If the annual

interest rate is $7\mathrm{.}2\%,$ how much money should you donate today? $(15$ points$)$