BUSI 422 Homework 1 TVM & Mortgage Calculations Assignment Liberty University
updated answers
Problem 4-18
A borrower and a lender agree on a $245,000 loan at 5 percent interest. An
amortization schedule of 25 years has been agreed on; however, the
lender has the option to “call” the loan after five years.
Required:
If called, how much will have to be paid by the borrower at the end of five
years?(Do not round intermediate calculations. Round your
final answer to 2 decimal places.)
Problem 4-15
A lender is considering what terms to allow on a loan. Current market terms
are 9 percent interest for 25 years for a fully amortizing loan. The borrower,
Rich, has requested a loan of $102,000. The lender believes that extra
credit analysis and careful loan control will have to be exercised because
Rich has never borrowed such a large sum before. In addition, the lender
expects that market rates will move upward very soon, perhaps even
before the loan is closed. To be on the safe side, the lender decides to
extend to Rich a CPM loan commitment for $96,900 at 9 percent interest
for 25 years; however, the lender wants to charge a loan origination fee to
make the mortgage loan yield 10 percent.
Required:
a. What origination fee should the lender charge?
b. What fee should be charged if it is expected that the loan will be repaid
after 10 years?
(For all requirements, do not round intermediate
calculations and round your final answers to 2 decimal
places.)
Problem 4-13
John wants to buy a property for $128,750 and wants an 80 percent loan
for $103,000. A lender indicates that a fully amortizing loan can be obtained
for 30 years (360 months) at 5 percent interest; however, a loan fee of
$5,400 will also be necessary for John to obtain the loan.
Required:
a. How much will the lender actually disburse?
b. What is the APR for the borrower, assuming that the mortgage is paid
off after 30 years (full term)?
c. If John pays off the loan after five years, what is the effective interest
rate?
d. Assume the lender also imposes a prepayment penalty of 2 percent of
the outstanding loan balance if the loan is repaid within eight years of
closing. If John repays the loan after five years with the prepayment
penalty, what is the effective interest rate?
Problem 4-11
A partially amortizing loan for $95,000 for 10 years is made at 7 percent
interest. The lender and borrower agree that payments will be monthly and
that a balance of $20,000 will remain and be repaid at the end of year 10.
Required:
a. Assuming 4 points are charged by the lender, what will be the yield if the
loan is repaid at the end of year 10?
b. What must the loan balance be if it is repaid after year 4?
c. What will be the yield to the lender if the loan is repaid at the end of year
4?
Note: For all requirements, do not round intermediate
calculations, round your final answers to 2 decimal places.
Problem 4-8
A fully amortizing mortgage is made for $90,000 for 25 years. Total monthly
payments will be $1,200 per month.
Required:
What is the interest rate on the loan?0(Round your final answer to 2
decimal places.)
Problem 4-7
A fully amortizing mortgage is made for $112,000 at 6.5 percent interest.
Required:
If the monthly payments are $1,060 per month, when will the loan be
repaid?0(Round up your answer to the nearest whole
number.)
Problem 4-6
A 30-year fully amortizing mortgage loan was made 10 years ago for
$88,000 at 6 percent interest. The borrower would like to prepay the
mortgage balance by $12,600.
Required:
a. Assuming he can reduce his monthly mortgage payments, what is the
new mortgage payment?
b. Assuming the loan maturity is shortened and using the original monthly
payments, what is the new loan maturity?
Problem 4-5
A fully amortizing mortgage loan is made for $105,000 at 6 percent interest
for 20 years.
Required:
a. Calculate the monthly payment for a CPM loan.
b. What will the0total0of payments be for the entire 20-year period? Of this
total, how much will be the interest?
c. Assume the loan is repaid at the end of eight years. What will be the
outstanding balance? How much total interest will have been collected by
then?
d. The borrower now chooses to reduce the loan balance by $5,500 at the
end of year 8.
(1) What will be the new loan maturity assuming that loan payments are not
reduced?
(2) Assume the loan maturity will not be reduced. What will the new
payments be?
Problem 4-4
A fully amortizing mortgage loan is made for $103,000 at 6 percent interest
for 30 years.
Required:
a. How much total interest would be paid over the entire 30-year life of the
mortgage, if interest is paid:
1. Monthly.
2. Quarterly
3. Annually
4. Weekly
(For all requirements, round your intermediate
calculations and final answers to 2 decimal places.)
b. Which payment pattern would have the greatest total amount of interest
over the 30-year term of the loan?
Problem 4-3
A fully amortizing mortgage loan is made for $116,000 at 6 percent interest
for 30 years.
Required:
a. Determine payments if interest is accrued monthly.
b. Determine payments if interest is accrued quarterly.
c. Determine payments if interest is accrued annually.
d. Determine payments if interest is accrued weekly.
Problem 4-2
A fully amortizing mortgage loan is made for $82,000 at 6 percent interest
for 25 years. Payments are to be made monthly.
Required:
a. Calculate monthly payments.
b. Calculate interest and principal payments during month 1.
c. Calculate total principal and total interest paid over 25 years.
d. Calculate the outstanding loan balance if the loan is repaid at the end of
year 10.
e. Calculate total monthly interest and principal payments through year 10.
f. What would the breakdown of interest and principal be during month 50?
Problem 4-1
A borrower obtains a fully amortizing CPM loan for $139,000 at 8 percent
interest for 10 years.
Required:
a. What will be the monthly payment on the loan?
b. If this loan had a maturity of 30 years, what would be the monthly
payment?
(For all requirements, do not round intermediate
calculations. round your final answers to 2 decimal
places.)
Problem 3-18
An investment is expected to produce the following annual year-end cash
flows:
Year 1$ 5,000.00
Year 2$ 1,181.00
Year 3 $ .00
Year 4$ 5,520.00
Year 5$ 6,340.00
Year 1$ 5,000.00
Year 6$ 1,544.16
The investment will cost $14,100 today.
Required:
a. Will this investment be profitable?
b. What will be the IRR (compounded annually) on this investment?
c. Show how much of each year’s cash flow is0recovery of0the $14,100
investment and how much of the cash flow is0return on0investment.
Problem 3-15
A loan of $73,600 is due 10 years from today. The borrower wants to make
annual payments at the end of each year into a sinking fund that will
earn0compound interestat anannual rate0of 10 percent.
Required:
a. What will the annual payments have to be?
Note: Do not round intermediate calculations and round
your final answer to 2 decimal places.
b. Suppose the investor makes the payments monthly instead.0 How much
would they need to pay each month?
Note: Do not round intermediate calculations and round
your final answer to 2 decimal places.
c. If payment was made by making monthly payments with monthly
compounding then how less they will pay in a year?
Note: Do not round intermediate calculations and round
your final answer to 2 decimal places.
Problem 3-14
A pension fund is making an investment of $104,000 today and expects to
receive $1,640 at the end of each month for the next five years. At the end
of the fifth year, the capital investment of $104,000 will be returned.
Required:
What is the internal rate of return0compounded annually0on this
investment?
Note: Do not round intermediate calculations and round
your final answer to 1 decimal place.
Problem 3-12
A corporation is considering the purchase of an interest in a real estate
syndication at a price of $76,000. In return, the syndication promises to pay
$1,020 at the end of each month for the next 25 years (300 months).
Required:
a. If the interest in a real estate syndication is purchased, what is the
expected internal rate of return,0compounded monthly?
Note: Do not round intermediate calculations and round
your final answer to 2 decimal places.
b. How much total cash would be received on the investment?
Note: Round your final answer to the nearest whole dollar
amount.
c1.0How much is profit?
Note: Round your final answer to the nearest whole dollar
amount.
c2.0How much is return of capital?
Note: Round your final answer to the nearest whole dollar
amount.
Problem 3-11
The Dallas Development Corporation is considering the purchase of an
apartment project for $116,000. They estimate that they will receive
$17,800 at the end of each year for the next 10 years. At the end of the
10th year, the apartment project will be worth nothing.
Required:
a. If Dallas purchases the project, what will be its internal rate of
return,0compounded annually?
Note: Do not round intermediate calculations and round
your final answer to 2 decimal places.
b. If the company insists on an 8 percent return0compounded
annually0on its investment, is this a good investment?
Problem 3-10
John is considering the purchase of a lot. He can buy the lot today and
expects the price to rise to $16,500 at the end of 10 years. He believes that
he should earn an investment yield of 8 percent0compounded
annually0on his investment. The asking price for the lot is $8,000.
Required:
a. What is the internal rate of return compounded annually on the
investment if John purchases the property for $8,000 and is able to sell it
10 years later for $16,500?
Note: Do not round your intermediate calculations and
round your final answer to 2 decimal places.
b. Should he buy the lot?
Problem 3-9
Walt is evaluating an investment that will provide the following returns at
the end of each of the following years: year 1, $12,800; year 2, $10,300;
year 3, $7,800; year 4, $5,300; year 5, $2,800; year 6, $0; and year 7,
$12,800. Walt believes that he should earn 12 percent compounded
annually on this investment.
Required:
a. How much should he pay for this investment?
b. How much should he pay if he expects to earn an annual return of 9
percent0compounded monthly?
Note: For all requirements, do not round PV factors and
round your other intermediate calculations and final
answer to the nearest whole dollar amount.
Problem 3-7
An investor is considering an investment that will pay $2,290 at the end of
each year for the next 10 years. He expects to earn a return of 12 percent
on his investment,0compounded annually.
Required:
a. How much should he pay today for the investment?
b. How much should he pay if the investment returns are received at
the0beginning of each year?
(For all requirements, do not round intermediate
calculations and round your final answers to the nearest
whole dollar amount.)
Problem 3-6
Suppose you have the opportunity to make an investment in a real estate
venture that expects to pay investors $890 at the end of each month for the
next eight years. You believe that a reasonable return on your investment
should be an annual rate of 15 percent0compounded monthly.
Required:
a. How much should you pay for the investment?
b. What will be the total sum of cash you will receive over the next eight
years?
c. What do we call the difference between the present value and total cash
received?
Note: For all requirements, do not round intermediate
calculations and round your final answers to the nearest
whole dollar amount.
Problem 3-5
Suppose you deposit $4,300 at the end of year 1, nothing at the end of
year 2, $930 at the end of year 3, and $1,480 at the end of year 4. Assume
that these amounts will be0compounded at an annual rate0of 15
percent.
Required:
How much will you have on deposit at the end of five years?
Note: Do not round PV factors and round your other
intermediate calculations and final answer to the nearest
whole dollar amount.
Problem 3-4
Suppose you deposit $2,250 at the end of each quarter in an account that
will earn interest at an annual rate of 8 percent0compounded quarterly.
Required:
How much will you have at the end of four years?
Note: Do not round intermediate calculations and round
your final answer to the nearest whole dollar amount.
Problem 3-3
Jones can deposit $6,200 at the end of each six-month period for the next
12 years and earn interest at an annual rate of 8 percent,0compounded
semiannually.
Required:
a. What will the value of the investment be after 12 years?
b. If the deposits were made at the beginning of each year, what would the
value of the investment be after 12 years?
Note: For all requirements, do not round intermediate
calculations and round your final answers to the nearest
whole dollar amount.
Problem 3-2
You would like to invest $26,700 for one year and are considering two
options. Investment A will earn interest at a rate of 7 percent compounded
monthly. Investment B will earn interest at a rate of 8 percent compounded
annually. (Hint: Consider one year only.)
Required:
a. What will be the value of Investment A?
Note: Do not round intermediate calculations and round
your final answer to the nearest whole dollar amount.
b. What will be the value of Investment B?
Note: Do not round intermediate calculations and round
your final answer to the nearest whole dollar amount.
c. Which investment would you prefer solely based on the value of
investment?
Problem 3-1
Jim makes a deposit of $13,300 in a bank account. The deposit is to earn
interest0compounded annually0at the rate of 7 percent for seven years.
Required:
a. How much will Jim have on deposit at the end of seven years?
(Hint:0What is future value?)
Note: Do not round intermediate calculations and round
your final answer to the nearest whole dollar amount.
b. Assuming the deposit earned a 10 percent rate of
interest0compounded quarterly, how much would he have at the end of
seven years?
Note: Do not round intermediate calculations and round
your final answer to the nearest whole dollar amount.
c1.0What is the0effective annual yieldfor alternative (a) where interest
is compounded annually? (Hint:0Consider the future value of each deposit
after one year only.)
Note: Do not round intermediate calculations and round
your final answer to 2 decimal places.
c2.0What is the0effective annual yieldfor alternative (b) where interest
is compounded quarterly? (Hint:0Consider the future value of each deposit
after one year only.)
Note: Do not round intermediate calculations and round
your final answer to 2 decimal places.
c3.0Which alternative is better?
