Week 5 Assignment 1) Would you rather have a savings account that pays 8% interest compounded semiannually or one that pays 4% interest compounded daily? Explain. 2) If you deposit $20,000 in a bank...

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Week 5 Assignment



1) Would you rather have a savings account that pays 8% interest compounded semiannually or


one that pays 4% interest compounded daily? Explain.



2) If you deposit $20,000 in a bank account that pays 10% interest annually, how much will


be in your account after 5 years?



3) What is the present value of a security that will pay $5,000 in 20 years if securities of equal


risk pay 7% annually?



4) What is the future value of a 7%, 10-year ordinary annuity that pays $300 each year? If this


were an annuity due, what would its future value be?



5) An investment will pay $100 at the end of each of the next 3 years, $200 at the end of Year


4, $300 at the end of Year 5, and $500 at the end of Year 6. If other investments of equal


risk earn 8% annually, what is this investment’s present value? Its future value?



6) Find the future values of the following ordinary annuities.



a. FV of $500 each 6 months for 5 years at a nominal rate of 15%, compounded



semiannually



b. FV of $250 each 3 months for 5 years at a nominal rate of 15%, compounded quarterly



c. The annuities described in parts a and b have the same total amount of money paid



into them during the 5-year period, and both earn interest at the same nominal rate,



yet the annuity in part b earns more than the one in part a over the 5 years.



Why does this occur?



7) Universal Bank pays 7% interest, compounded annually, on time deposits. Regional Bank


pays 6.9% interest, compounded quarterly.



a. Based on effective interest rates, in which bank would you prefer to deposit your money?



b. Could your choice of banks be influenced by the fact that you might want to



withdraw your funds during the year as opposed to at the end of the year? In



answering this question, assume that funds must be left on deposit during an entire



compounding period in order for you to receive any interest.



8) Washington-Pacific invested $5 million to buy a tract of land and plant some young pine


trees. The trees can be harvested in 10 years, at which time W-P plans to sell the forest at


an expected price of $9 million. What is W-P’s expected rate of return?



9) While AJ was a student at the University of Texas, she borrowed $30,000


in student loans at an annual interest rate of 9%. If Mary repays $1,500 per year, then how


long (to the nearest year) will it take her to repay the loan?



10) You have $60,000 to put as a down payment on a new house that costs $600,000, and you have been quoted the following terms: 5% Annual Percentage Rate (APR), for 30 years. If you decide to purchase this home, what will your monthly payment be? Additionally, over the life of the loan what would your total interest expense be?


11) The present value (t = 0) of the following cash flow stream is $15,000 when discounted at 12 percent an­nually. What is the value of the missing t = 2 cash flow?




0 1 2 3 4



| | | | |



PV = $15,000 2,000 ? 4,000 4,000




12) Assume that you inherited some money. A friend of yours is working as an unpaid intern at a


local brokerage firm, and her boss is selling securities that call for 4 payments of $200 (1


payment at the end of each of the next 4 years) plus an extra payment of $2,000 at the end of


Year 4. Your friend says she can get you some of these securities at a cost of $2500 each. Your money is now invested in a bank that pays an 8% nominal (quoted) interest rate but with quarterly compounding. You regard the securities as being just as safe, and as liquid, as your bank deposit, so your required effective annual rate of return on the securities is the same as that on your bank deposit. Should you buy these securities at a cost of $2500 each?


Answered Same DayMar 01, 2021

Answer To: Week 5 Assignment 1) Would you rather have a savings account that pays 8% interest compounded...

Tanmoy answered on Mar 02 2021
138 Votes
Week 5 Assignment
1) Would you rather have a savings account that pays 8% interest compounded semi-annually or one that pays 4% interest compounded daily? Explain
A 365 compounding period on a daily basis will generate more money than an account which requires semi-annual c
ompounding which is twice in a year. But an exception will occur if the interest rate for the semi-annual compounding period is high. Below are the workings:
    Compounding Semi-annually
    Principal
    5000
    Annual Interest Rate
    8%
    Compounding Period per year
    2
    Years
    1
    Investment Value
    $5,408

Calculation process in excel: = FV (8%/2, 2 x 1, 0, -5000) = $5408
    Compounding daily
    Principal
    5000
    Annual Interest Rate
    4%
    Compounding Period per year
    1
    Years
    1
    Investment
    $5,204
Calculation process in excel: = 5000 x (1 + 4%/365) ^ (1 x 365) = $5204
Thus based on the above analysis we can see that compounding semi-annually at 8% gives more amount of $5408 than compounding daily interest with 4% i.e., $5204. We have used excel formula which to calculate the investment values of compounded semi-annually i.e. =FV (Annual Interest Rate/ compounding period per year, compounding period per year * years, 0, -Principal). For the compounding daily we have used the formula Principal * (1+annual interest rate/365) ^ (Years * 365)
2) If you deposit $20,000 in a bank account that pays 10% interest annually, how much will be in your account after 5 years?
    Amount with Principal + Interest
    Amount
    20000
    Interest Annually
    10%
    Years
    5
    Future Value
    32210
The future value or the amount is calculated using excel as: 20000*(1+0.10) ^5 = $32210
3) What is the present value of a security that will pay $5,000 in 20 years if securities of equal risk pay 7% annually?
    PV of security
    Principal
    5000
    Years
    20
    Interest
    7%
    PV
    0.26
    PV of Cash flows
    1292
The PV of cash flow is calculated in excel using the formula: $5000*[1/ (1+0.07) ^20] = $1292
4) What is the future value of a 7%, 10-year ordinary annuity that pays $300 each year? If this were an annuity due, what would its future value be?
    Ordinary Annuity
    Amount
    300
    Interest
    7%
    Years
    10
    Future Value
    $4,145
Calculation in excel: Future Value (7%, 10, -300,, 0) = $4145
    Annuity Due Amount
    Amount
    300
    Interest
    7%
    Years
    10
    Future Value
    $4,435
Calculation in excel: Future Value (7%, 10, -300,,1) = $4435
5) An investment will pay $100 at the end of each of the next 3 years, $200 at the end of Year 4, $300 at the end of Year 5, and $500 at the end of Year 6. If other investments of equal risk earn 8% annually, what is this investment’s present value? Its future value?
    Years
    Cash Flows
    PV @ 8%
    PV of...
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