$1.$ Suppose for an annuity due you want to have $$30000$ in the bank after $20$

years Assuming you deposit at the beginning of each year at an interest rate

of $4\%.$ How much do you have to deposit at the start of each year assuming

each deposit is the same amount?

$2.$ A company is considering a project that requires an investment of $ $120,000$

in Machinery. The machinery will last four years after which it will have a

scrap value of $ $20000.$ The investment in additional working capital will be $

$15,000.$

The expected annual profits before depreciation is

Year Amount$($$$)$

$145000$

$245000$

$340000$

$425000$

The company requires a minimum accounting rate of return of $15\%$ from projects of this

type. ARR is measured as the average annual profits percentage of the average investment.

Should the project be undertaken?

$3.$ Elina wishes to purchase an apartment at Auasbrick which costs $$710000\mathrm{.}00.$

She can get a $100\%$ mortgage loan at the interest of $6\%$ compounded

monthly. The term of her loan is $20$ years. Assuming the property value rises

to a rate of $9\%$ per year $(0\mathrm{.}75\%$ per month$).$ She then decided to rent out the

apartment for $ $4000$ after cost per month for the first year. Interest and rent

are payable at the beginning of each month.

Required to:

What is the expected value of the apartment in $20$ years? What is the

mortgage loan repayment at the beginning of each month? What is the net

amount she has to pay in each month?