1. Find the interest rate (or rates of return) for each of the following situati

Question

1. Find the interest rate (or rates of return) for each of the following situations. Round your answers to two decimal places.

a) You borrow $65,000 and promise to pay back $180,547 at the end of 14 years.

b) You borrow $10,000 and promise to make payments of $2,445.7 at the end of each year for 5 years.

2. Find the present value of the following ordinary annuities. Round your answers to the nearest cent.

**payments are made at the beginning of each year; that is, they are annuities due.**

a) $800 per year for 10 years at 8%.

b) $400 per year for 5 years at 4%.

3. The real risk-free rate of interest is 3%. Inflation is expected to be 1% this year and 6% during the next 2 years. Assume that the maturity risk premium is zero.

a) What is the yield on 3-year Treasury securities? Round your answer to two decimal places.

4. The Garraty Company has two bond issues outstanding. Both bonds pay $100 annual interest plus $1,000 at maturity. Bond L has a maturity of 15 years, and Bond S has a maturity of 1 year.

a) What will be the value of each of these bonds when the going rate of interest is 14%? Assume that there is only one more interest payment to be made on Bond S. Round your answers to the nearest cent.

What is Bond L? ______

Thank you.

Explanation / Answer

1. CALCULATION OF INTEREST RATES:

(a)AMOUNT BORROWED(P)=$65,000

PAY BACK(A)=$1,80,547

TIME(T)=14 YEARS

INTEREST(I)=$1,80,547-$65,000=$1,15,547

LET INTEREST RATE=R

APPLYING FORMULA,

I=(P*R*T)/100

OR,$1,15,547=($65,000*R*14)/100

OR,$1,15,547=$9,100R

OR,R=$1,15,547/$9,100

OR,R=12.70%

INTEREST RATE=12.07%

(b)b) You borrow $10,000 and promise to make payments of $2,445.7 at the end of each year for 5 years

AMOUNT BORROWED(P)=$10,000

PAYMENT AT THE END OF EACH MONTH=$2,445.7

TIME(T)=5 YEARS

$10,000 IS THE PRESENT VALUE OF PAYMENTS OF $2,445.7 MADE AT THE END OF EACH OF 5 YEARS DISCOUNTED AT THE INTEREST RATE

HENCE,$10,000=2,445.7PVIFA(R%,5)

2.CALCULATION OF PRESENT VALUE

(a)PRESENT VALUE=$800+$800PVIFA(8%,9)

=$800+$800*6.247

=$5,797.6

(b)PRESENT VALUE=$400+$400PVIFA(4%,4)

=$400+$400*3.630

=$1,852

3.RISK FREE INTEREST RATE=3%

INFLATION RATE IN PRESENT YEAR=1%

IN YEAR 2=6%

IN YEAR 3=6%

YIELD ON 3 YEARS TREASURY SECURITY =3*1.01*1.06*1.06=3.4%

4.CALCULATION OF VALUE OF BONDS

VALUE OF BOND L=$100PVIFA(14%,15)+$1,000PVIF(14%,15)

=$100* 6.142 +$1,000*0.140

=$614.2+$140

=$754.2

VALUE OF BOND S=$100PVIF(14%,1)+$1,000PVIF(14%,1)

=$100*0.877+$1,000*0.877

=$87.7+$877

=$964.7

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