Find the loan interest rate as a nominal annual rate

Assignment Help Mathematics

Reference no: EM132297257

Math Problems -

(1) A Treasury Bill with 90-day maturity, maturing with the value of $10,000, sells at a quoted rate of 3%. Calculate the difference between the price of this T-bill in the case when it is a United States T-Bill and the price of it in the case when it is a Canadian Government T-Bill.

(A) More than $5

(B) $5 or less but more than $2.50

(D) $0 or less but no less than -$2.50

(E) -$2.50 or less

(2) An investor deposits 50 in an investment account on January 1. The following summarizes the activity in the account during the year:

Date	Value immediately before deposit	Deposit
March 15	40	20
June 1	80	80
October 1	175	75

On June 30, the value of the account is 157.50. On December 31, the value of the account is X. Using the time-weighted method, the equivalent annual effective yield during the first six months is equal to the time-weighted annual effective yield during the entire one-year period. Calculate X.

(A) 234.75

(B) 235.50

(D) 237

(E) 237.75

(3) Consider a perpetuity, which make payments twice a year. The first-year payments are 5 at time 0.5 years and 5 at time 1, next year they are 10 at time 1.5 years and 10 at time 2, in the third year the payments are 15 at time 2.5 years and 15 at time 3, and so on. The annual interest rate is 8% nominal convertible semiannually. Find the present value of this perpetuity.

(A) 125

(B) 1250

(D) 2325

(E) 2567

(4) An insurance company has an investment portfolio that consists of three types of bonds:

(i) Ten-year bond with annual coupon of 10%,

(ii) Twenty-year zero-coupon bond,

(iii) A perpetuity immediate making annual payments.

You are given that the interest rate is 10%. Find the fraction of the portfolio invested in the ten-year bond if you are given that the Macaulay duration of the entire portfolio is 12.00, while the Macaulay duration of the portion of the portfolio excluding the ten-year bond is 15.50.

(A) Less than 40%

(B) At least 40% but no more than 43%

(D) At least 46% but no more than 49%

(E) 49% or more

(5) Given the following information about bonds with coupons paid annually

Bond	Par value	Time to Maturity (in years)	Annual coupon Rate	Bond price
1	$100	1	0%	$95.12
2	$100	2	0%	unknown
3	$100	3	0%	$78.66
4	$100	3	5%	$91.72

Find the forward rate from time 2 to time 3.

(A) Less than 5%

(B) 5% or more but less than 7%

(D) 9% or more but less than 11%

(E) 11% or more

(6) Find the convexity of a portfolio consisting of the following instruments, assuming the effective rate of interest is 8%:

(a) A million dollars investment in a ten-year zero-coupon bond.

(b) A million dollar investment in a $1000 par value 3-year bond with 10% annual coupons.

(A) Less than 100

(B) 100 or more but less than 175

(D) 250 or more but less than 313

(E) 313 or more

(7) A senior executive is offered a buyout package by his company that will pay him a monthly benefit for the next twenty years. Monthly benefits will remain constant within each of the twenty years. At the end of each 12-month period, the monthly benefits will be adjusted upwards to reflect the percentage increase in the Consumer Price Index (CPI). You are given that the first monthly benefit is R and will be paid one month from today and that the CPI increases 3.2% per year forever. At an annual effective interest rate of 6%, the buyout package has a value of 100,000. Calculate R.

(A) 517

(B) 538

(D) 548

(E) 563

(8) A callable bond paying annual coupons of 5% can be redeemed at par on a coupon date, just after a coupon payment, anytime between ten and twenty coupon periods from now. If the bond is called at a most advantageous time for its issuer, what is the yield that will be earned by an investor who has just purchased the bond at a premium of 10% over par? Assume that interest rates will remain unchanged for the next twenty coupon periods.

(A) 3.5%

(B) 3.75%

(D) 4.25%

(E) 4.5%

(9) A loan of amount L is to be repaid by ten annual payments beginning one year after the loan is made. The level payment in the final five years is double the level payment in the, first five years. The principal outstanding just after the seventh payment is?

(10) A mortgage loan had level monthly payments for thirty years, with the first payment due one month after the loan is made. It is found that the total principle repaid in the first twenty years of the loan is 80% of the principle repaid in the final ten years of the loan. Find the loan interest rate as a nominal annual rate compounded monthly.

(A) 5.85%

(B) 6.00%

(D) 6.47%

(E) 6.83%

(11) Penney Airlines entered into a five-year interest rate swap two years ago. Under the five-year swap, Penney agreed to be the payer of a swap rate of 6.5% ona level annual notional amount of 100,000 each year for five years. Now there are three years left on the swap agreement. Today, the spot interest rates are

Years to maturity	1	2	3	4	5
Spot Rate	0.05	0.057	0.065	0.075	0.08

Calculate the market value of the swap from Penney's perspective if Penney decided to sell it today.

(A) -174.26

(B) -86.45

(D) 86.45

(E) 174.26

(12) The swap curve for interest rate swaps that swap floating interest for fixed interest has the following swap rates (annual effective rates)

Term	1-year	2- year	3-year	4-year
Swap Rate	5%	5.3%	5.5%	5.5%

Find the one-year forward two year deferred annual effective rate of interest.

(A) Less than 0.055

(B) At least 0.055, but less than 0.057

(D) At least 0.059 but less than 0.061

(E) At least 0.061

Note - Don't need excel spreadsheet solutions. Want written solutions including all applicable formulas.

Reference no: EM132297257

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