FIN301 Sessions 15 and 16

10 Years ago you took out a 30-year mortgage to buy a house. Your annual payment is $18,162 and your current interest rate is 6%. Suppose you now want to refinance and still pay off the house in 20 years, how much principal do you still owe on the mortgage? A. $208,316.71 B. $668,099.91 C. $363,240.00 D. $341,445.60 E. $133,673.90

A. $208,316.71 ==Future Value N=20 I=6 PMT= 18162 FV=0

Jim wants to buy a $500,000 house, he already has $10,000 saved. Assuming a 10% annual return and a 30% tax rate, how much will Jim need to save per year to have a 20% down payment in 3 years? A. $27,295 B. $26,190 C. $38,803 D. $40,211 E. $150,136

A. $27,295 20%(500,000)=100,000=FV PV= -10,000 N= 3 I= 10(1-30%)= 7

Suppose you win $1,500, approximately how long it will take for your winnings to reach $4,000 in value if your annual investment returns are 10% (tax-free)? A. 10 years B. 72 years C. 7 years D. 5 years E. 15 years

A. 10 years PV= 1500 FV= 4000 I= 10 PMT= 0

Kevin's parents have $10,000 saved for his college education. His parents invested the $10,000 and it grew to $100,000 at the end of 20 years. What annual interest rate did they earn if we assume compounding interest? A. 12% B. 20% C. 8% D. 10% E. 5%

A. 12%

You invest $150 today and in 5 years you will have $300. Ignoring taxes, what is the annual return on your investment? A. 14.9% B. 37.5% C. 50% D. 100%

A. 14.9% I/Y calculator or input negative future value and 0 for PMT in calculator

Your uncle needs $2,300,000 upon retirement in 30 years to live comfortably. He can invest $18,500 a year to his retirement. What interest rate would his investment need to appreciate at in order for him to meet his goals? A. 8.5% B. 13.8% C. 11.7% D. 4.1% E. 16.3%

A. 8.5% Plug into calculator and put PV=0 and PMT negative

If you invest $130 today and, in 5 years, you have $200 - what was your annually compounded interest? Ignore taxes. A. 9.0% B. 20% C. 53.85% D. 70%

A. 9.0% N=5 PMT=0 PV= 130 FV= -200

When determining a discount rate, what two factors should be taken into consideration? A. Risk & Time B. Time & Dollar Amount C. Dollar Amount & Risk D. Risk & Return E. Time & Return

A. Risk & Time

On January 1 of this year, you invested $350 at a rate of 5% compounded annually. If your tax rate is 30%, what will the tax on your investment be at the end of the year? A. $5 B. $5.25 C. $17.5 D. $105 E. $175

B. $5.25

Assuming a 6% discount rate, how much would you need to invest now to have $100,000 in 10 years with no additional investment? A. $23,299.86 B. $55,839.48 C. $94,000.00 D. $38,554.33 E. $75,867.96

B. $55,839.48

You invest $220 at 15% compounded annually. If your tax rate is 30%, what is your after-tax annual rate? A. 4.5% B. 10.5% C. 15% D. 33% E. 45%

B. 10.5% After Tax = 0.15(1-.30)

If you had the option of $2,000 in 5 years or $1,000 today, you would take the money today if your expected return was less than: A. 20.0% B. 14.9% C. 1.5% D. 10.0% E. 23.5%

B. 14.9% N= 5 PV= 1000 PMT=0 FV= -2000

If you invest $3,000 in a start-up and 5 years later your investment is worth $30,000, what was the annual rate of return on this investment? A. 1,000% B. 58.5% C. 200.0% D. 64.6% E. 82.3%

B. 58.5% Plug into calculator, make FV negative and plug in 0 for PMT

You have 24 years left until you retire and you plan on buying yourself a new $20,000 car on the day you retire. If you invest $300 a year for the next 24 years earning 4% a year - will you have enough money? A. Yes B. No

B. No 11,724.7812

Nate invested $1,200,000 in Melco Crown. He held the stock for 6 years, and the stock returned 15% annually. How much money did Nate make before taxes? A. $1,867,534 B. $1,575,673 C. $2,775,673 D. $3,067,534 E. None of the Above

C. $2,775,673

Randy invested $87,000 in securities that had an annual return of 13%. When Randy sold his investment, the securities had a value of $295,327. How long did Randy hold the securities? A. 8 years B. 13 years C. 10 years D. None of the Above

C. 10 years

Suppose you have the choice between receiving $500 now, or $750 in 3 years. What discount rate would make these options worth the same to you? A. 4.82% B. 5.56% C. 14.47% D. 16.67% E. 43.65%

C. 14.47%

If your $325 investment collects simple interest of 10%, how much will it be worth in 6 years? A. $32.50 B. $60 C. 520 D. 566.90

C. 520 ((325(.10))x6)+325=520

Which of the following is CERTAINLY true regarding interest rates? A. Increases in interest rates lead to increases in stock prices. B. Increases in interest rates lead to increases in bond prices. C. Increases in interest rates lead to decreases in bond prices. D. The effect of a change in interest rates on bond and stock prices is unknown. E. Interest rates do not affect stock or bond prices.

C. Increases in interest rates lead to decreases in bond prices.

Which of the following is true concerning the difference between simple and compound interest? A. With compound interest, interest is earned only on the original investment whereas with simple interest, interest is earned on interest. B. Simple interest always leads to a higher ending investment value when compared to compound interest. C. With simple interest, interest is earned only on the original investment whereas with compound interest, interest is earned on both the original investment and the accumulated interest. D. With compound interest, the assumption is that interest earned on the original investment is not reinvested. With simple interest, interest is reinvested. E. Simple interest and compound interest always lead to the same ending investment value so there is no difference between the two methods.

C. With simple interest, interest is earned only on the original investment whereas with compound interest, interest is earned on both the original investment and the accumulated interest.

Tina needs $100,000 a year for 25 years to retire comfortably, assuming she can earn an 8% return on her retirement portfolio, how much does she need to retire? A. $1,082,079.41 B. $981,814.74 C. $2,500,000.00 D. $1,067,477.62 E. $2,300,000.00

D. $1,067,477.62 ===PV N= 25 I= 8 PMT= 100,000 FV= 0

You have an annuity with expected $50,000 payments each year for 20 years. If the discount rate is 8%, what is the present value of this annuity? A. $351,677 B. $500,101 C. $1,000,000 D. $490,907 E. $367,056

D. $490,907

Joe invested $75,000 in Kaiser Aluminum. When he sold the stock, his shares were worth a total value of $127,000 and the stock returned 13% annually. How long did Joe hold the stock? A. 2 years B. 3.7 years C. 5 years D. 4.3 years E. None of the Above

D. 4.3 years

At the beginning of the year, you invested $300 at a rate of 10% compounded annually. At the end of the year, you will have to pay a $12 tax on your investment. What is your tax rate? A. 4% B. 12% C. 30% D. 40%

D. 40% 300+(300*10%)=330-300=30 12/30=.40

John won the lottery and has the option to receive a lump sum of $5,000,000 now or receive a $500,000 annuity every year for the next 25 years. Assuming John can earn a 10% return on his money, what would you advise him to do? A. Take the annuity because it is worth $50,840 more than the lump sum B. Take the lump sum because it is worth $50,840 more than the annuity C. Take the annuity because it is worth $461,480 more than the lump sum D. Take the lump sum because it is worth $461,480 more than the annuity E. Whatever he wants, both are worth the same.

D. Take the lump sum because it is worth $461,480 more than the annuity

Travis took out a $225,000 home mortgage with 3.4% interest rate and equal annual payments. How much will he have to pay annually to repay the loan in 15 years? A. $9,084 B. $7,650 C. $5,995 D. $15,000 E. $19,397

E. $19,397 loan calculator or PVMP table= round and then guess

If you invest $5,100 a year, what would be the value of this investment at the end of 4 years at an interest rate of 7.75% and a tax rate of 17%? A. $16,986 B. $14,099 C. $19,004 D. $18,968 E. $22,454

E. $22,454 7.75 x (1-.17) = I N=4 PMT= -5100 PV=0

If you invest $15,000 today at a rate of 8.75% (tax-free), how much will it be worth 40 years from now? A. $118,613 B. $317,556 C. $551,724 D. $652,500 E. $429,796

E. $429,796 enter into calculator but came out negative

What interest rate would you have to earn if you wanted to double an investment in 25 years? A. 9.2% B. 13.7% C. 11.1% D. 4.8% E. 2.9%

E. 2.9% 72/25=2.88

Dan puts $100 into a savings account that earns 5% (tax-free) interest. In 5 years, he has $105 in the account. Dan earned compounded interest on his principal investment.

False

The rule of 72 works for single payments and for annuities.

False

True or False: A higher discount rate will increase the present value of an annuity.

False

True or False: As market interest rates rise, the value of bonds rise as well.

False

True or False: As the discount rate falls, present value falls.

False

True or False: Discount rates are generally negative numbers.

False

True or False: Investment A and B have the same future value and discount rate; however, investment A has a holding period of 6 years (n=6) while investment B has a holding period of 4 years (n=4). Given that information, investment B has a lower present value than investment A.

False

True or False: More frequent compounding is bad for investors because it leads to higher costs and lowers their overall return.

False More = Better

True or False: $60 invested at 15% compounded annually will be worth more in 5 years than $80 invested at 8% compounded annually.

True

True or False: Assuming a 10% discount rate, you would have to invest $77,108.66 now in order to have $200,000 at the end of 10 years.

True

When you discount, you multiply by a number less than 1.0.

True