BUSI 422 Homework 1 TVM & Mortgage Calculations Assignment solutions complete answers

BUSI 422 Homework 1 TVM & Mortgage Calculations Assignment solutions complete answers 

 

Just put your values given and automatically provide answers for you!

 

Jim makes a deposit of $13,600 in a bank account. The deposit is to earn interest compounded annually at the rate of 6 percent for seven years.

a. How much will Jim have on deposit at the end of seven years? (Hint: What is future value?)

b. Assuming the deposit earned a 9 percent rate of interest compounded quarterly, how much would he have at the end of seven years?

c1. What is the effective annual yield for alternative (a) where interest is compounded annually? (Hint: Consider the future value of each deposit after one year only.)

c2. What is the effective annual yield for alternative (b) where interest is compounded quarterly? (Hint: Consider the future value of each deposit after one year only.)

c3. Which alternative is better?

 

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.)

a. What will be the value of Investment A?

b. What will be the value of Investment B?

c. Which investment would you prefer solely based on the value of investment?

 

Jones can deposit $6,400 at the end of each six-month period for the next 12 years and earn interest at an annual rate of 8 percent, compounded semiannually.

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?

a. Future value of annuity

b. Future value of annuity due

 

Suppose you deposit $3,150 at the end of each quarter in an account that will earn interest at an annual rate of 9 percent compounded quarterly.

How much will you have at the end of four years?

 

Suppose you deposit $3,800 at the end of year 1, nothing at the end of year 2, $880 at the end of year 3, and $1,430 at the end of year 4. Assume that these amounts will be compounded at an annual rate of 13 percent.

How much will you have on deposit at the end of five years?

 

Suppose you have the opportunity to make an investment in a real estate venture that expects to pay investors $830 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 percent compounded monthly.

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?

 

An investor is considering an investment that will pay $2,230 at the end of each year for the next 10 years. He expects to earn a return of 12 percent on his investment, compounded annually.

a. How much should he pay today for the investment?

b. How much should he pay if the investment returns are received at the beginning of each year?

 

Walt is evaluating an investment that will provide the following returns at the end of each of the following years: year 1, $14,400; year 2, $11,900; year 3, $9,400; year 4, $6,900; year 5, $4,400; year 6, $0; and year 7, $14,400. Walt believes that he should earn 12 percent compounded annually on this investment.

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 percent compounded monthly?

 

John is considering the purchase of a lot. He can buy the lot today and expects the price to rise to $15,400 at the end of 10 years. He believes that he should earn an investment yield of 8 percent compounded annually on his investment. The asking price for the lot is $8,000.

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 $15,400?

b. Should he buy the lot?

 

The Dallas Development Corporation is considering the purchase of an apartment project for $110,000. They estimate that they will receive $16,750 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.

a. If Dallas purchases the project, what will be its internal rate of return, compounded annually?

b. If the company insists on an 8 percent return compounded annually on its investment, is this a good investment?

 

A corporation is considering the purchase of an interest in a real estate syndication at a price of $82,000. In return, the syndication promises to pay $1,140 at the end of each month for the next 25 years (300 months).

a. If the interest in a real estate syndication is purchased, what is the expected internal rate of return, compounded monthly?

b. How much total cash would be received on the investment?

c1. How much is profit?

c2. How much is return of capital?

 

A pension fund is making an investment of $118,000 today and expects to receive $1,780 at the end of each month for the next five years. At the end of the fifth year, the capital investment of $118,000 will be returned.

What is the internal rate of return compounded annually on this investment?

 

A loan of $71,900 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 earn compound interest at an annual rate of 10 percent.

a. What will the annual payments have to be?

b. Suppose the investor makes the payments monthly instead.  How much would they need to pay each month?

c. If payment was made by making monthly payments with monthly compounding then how less they will pay in a year?

 

An investment is expected to produce the following annual year-end cash flows:

The investment will cost $14,100 today.

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 is recovery of the $14,100 investment and how much of the cash flow is return on investment. (Hint: See Exhibit 3-13 and Concept Box 3.2.)

 

A borrower obtains a fully amortizing CPM loan for $133,000 at 6 percent interest for 10 years.

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?

 

A fully amortizing mortgage loan is made for $83,000 at 6 percent interest for 25 years. Payments are to be made monthly.

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?

 

A fully amortizing mortgage loan is made for $102,000 at 6 percent interest for 30 years.

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.

 

A fully amortizing mortgage loan is made for $103,000 at 6 percent interest for 30 years.

a. How much total interest would be paid over the entire 30-year life of the mortgage, if interest is paid:

b. Which payment pattern would have the greatest total amount of interest over the 30-year term of the loan?

 

A fully amortizing mortgage loan is made for $107,000 at 6 percent interest for 20 years.

a. Calculate the monthly payment for a CPM loan.

b. What will the total of 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 $5,700 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?

 

A 30-year fully amortizing mortgage loan was made 10 years ago for $93,000 at 6 percent interest. The borrower would like to prepay the mortgage balance by $13,600.

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?

 

A fully amortizing mortgage is made for $124,000 at 6.5 percent interest.

If the monthly payments are $1,120 per month, when will the loan be repaid? (Round up your answer to the nearest whole number.)

 

A fully amortizing mortgage is made for $89,000 for 25 years. Total monthly payments will be $1,170 per month.

What is the interest rate on the loan? (Round your final answer to 2 decimal places.)

 

A partially amortizing loan for $94,000 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.

a. Assuming 3 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?

 

John wants to buy a property for $116,250 and wants an 80 percent loan for $93,000. A lender indicates that a fully amortizing loan can be obtained for 30 years (360 months) at 8 percent interest; however, a loan fee of $4,400 will also be necessary for John to obtain the loan.

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?

 

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 $115,000. 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 $109,250 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.

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?

 

A borrower and a lender agree on a $285,000 loan at 8 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.

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.)