Question $1.(20$ marks$)$

$($a$)($i$)$ Mr$.$ Moore is $35$ years old today and is beginning to plan for his retirement. He

wants to set aside an equal amount at the end of each of the next $25$ years so that

he can retire at age $60.$ He expects to live to the maximum age of $80$ and wants to

withdraw $$25,000$ per year from the account on his $61$ st through $80$ th birthdays.

The account is expected to earn $10\%$ per annum for the entire period of time.

Determine the size of the annual deposits that he must make.

$(3$ marks$)$

$($ii$)$ A bank has agreed to loan you $$10,000$ at $11\%$ for $5$ years. You are required to

make equal, annual, end$-$of$-$year payments that include both principal and interest

on the outstanding balance. Determine the amount of these annual payments $($to

the nearest dollar$).$ After making the third payment, how much interest in total

would you have paid on the loan?

$(5$ marks$)$

$($iii$)$ Your local bank offers $4-$year certificates of deposit $($CD$)$ at a $12$ percent annual

nominal interest rate compounded quarterly. Determine how much additional

interest you will earn over $4$ years on a $$10,000CD$ that is compounded quarterly

compared with one that is compounded annually.

$(4$ marks$)$

$($iv$)$ Inco purchased a computer for $$200,000$ and this machine is expected to generate

annual cash flows of $$48,271$ over the next $5$ years. What is the expected rate of

return on this investment?

$(2$ marks$)$

$($b$)($i$)$ Differentiate between the nominal and the effective interest rates?

$(3$ marks$)$

$($ii$)$ Define a perpetuity and give three examples of such investments.

$(3$ marks$)$

Ouestion $2.(20$ marks$)$