Practice Exam $1-$ Exam FM

Page PE$1-5$

$20.$ A woman buys a $1,000-$par $5-$year zero$-$coupon bond priced to yield $6\%.$ At the same time she buys a $1,000-$par $5-$year bond with $8\%$ semi$-$annual coupons that is priced to yield $7\%$ convertible semi$-$annually. The coupon payments are reinvested at $6\mathrm{.}5\%$ convertible semi$-$annually. What is her annual effective yield for the combination of these investments?

A$)6\mathrm{.}0\%$

B$)6\mathrm{.}2\%$

C$)6\mathrm{.}4\%$

D$)6\mathrm{.}6\%$

E$)6\mathrm{.}8\%$

$21.$ Account A earns compound interest at an annual effective rate $i($where $i$ is greater than $0).$ Account B earns compound interest at an annual effective rate equal to $1\mathrm{.}1*i$

An amount of $1,000$ is deposited into each of these accounts at $t=0.$ No other deposits or withdrawals occur. At the end of $20$ years $($at $t=20),$ the balance in Account B will be $10\%$ larger than the balance in the Account A$.$

What will be the difference between the balances in the two accounts at the end of $10$ years $($at $t=10?$

A$)75$

B$)80$

C$)85$

D$)90$

E$)95$

$22.$ A homebuyer borrows $200,000$ under a $20-$year variable$-$rate mortgage with monthly payments. The initial interest rate for this mortgage loan is $3\mathrm{.}6\%($compounded monthly$).$

At the end of $2$ years, the mortgage interest rate increases from $3\mathrm{.}6\%$ to $4\mathrm{.}5\%$ and a new monthly payment amount $($for the $3^{rd}$ and later years$)$ is calculated, based on the new interest rate and the outstanding loan balance on that date. There are no other interest rate changes during the first $5$ years of the loan.

To the nearest $100,$ what is the outstanding balance of the loan at the end of $5$ years $($immediately after the ${60}^{th}$ monthly payment$)?$

A$)162,600$

B$)162,900$

C$)164,000$

D$)164,300$

E$)165,400$

$23.$ A $20-$year bond has a face amount $($and maturity value$)$ of $1,000.$ It pays semi$-$annual coupons at a $6\%($annual$)$ coupon rate. The bond is callable on any coupon date on or after its ${10}^{th}$ anniversary, with a $5\%$ call premium.

If an investor purchases this bond on its issue date at a price of $1,060,$ and holds the bond until it matures or is called, what is the minimum yield that the investor could earn $($expressed as a nominal rate, convertible semiannually$)?$

A$)5\mathrm{.}50\%$

B$)5\mathrm{.}59\%$

C$)5\mathrm{.}76\%$

D$)5\mathrm{.}96\%$

E$)6\mathrm{.}37\%$

ACTEX Learning

Dinius, Hassett, Ratliff, Garcia, & Steeby

Exam FM $-$ Financial Mathematics