ECON 2210 – KPU Copyright: Rabia Aziz Spring Homework Assignment Ch 4 1. Consider a situation in which you take loan from a bank worth $200,000 to buy a house. The fixed-rate mortgage gives you 30 years to pay the loan at an annual rate of 8%. a) Calculate the value for the annual payment that you must pay under this contract. b) What will be the monthly payment? 2 Calculate the YTM on each of the following three bonds: i. Bond A – has a price of $900 and pays $20 dollars of interest annually forever ii. Bond B – has a price of $950, Face Value of $1000 and 1 years to maturity iii. Bond C – has a price of $950, Face Value of $1000 and 2 years to maturity iv. Bond D – has a price of $890, Face Value of $1000, coupon rate of 5% and 10 years to maturity 3 Calculate your capital gains and holding period return if you hold for 1 year i. a 10%-coupon-rate bond with 10-year maturity and $1000 face value, which you bought at par this year, if the interest rate falls next year from 10% to 7%. ii. A bond with current price of $500 and pays $50 annually forever, if interest rate falls from 10% to 7% iii. Government of Canada T-bill currently selling for $1502.63, matures in 3 years and has a Face Value of $2000, if interest rate falls next year from 10% to 7% Given your answers which bond would you want to hold if you expect interest rates to fall from 10% to 7% next year. [Note: you will have to calculate price after 1 year for each of these in order to calculate capital gains and Return after 1 year]
Money and Banking
Question One
- The loan is $200,000, which will be paid at a fixed rate of 30 years and an annual rate of 8%.
The formula for annual payment= a/{[1+r) ^n] -1}/[r(1+r) ^n] where;
a is the mortgage amount
r is the interest rate
n is the number of annual payments
Calculation:
200,000/ {[1+0.08) ^30]-1}/ [0.08(1+0.08) ^30] = 27,414.39
This answer means that I will make an annual payment of $27,414 to the bank under this contract.
- If I make an annual payment under the rate of 8%, it implies that the monthly rate is 6% (8%/12 months). Furthermore, I will make the payments monthly, suggesting that the number payment is 360.
Therefore, the monthly payment is: 200,000/ {[1+0.06) ^360]-1}/ [0.06(1+0.06) ^360] = 2,280
This answer implies that I will pay $2,280 monthly under this contract.
Question Two
The yield to maturity (YTM) is the expected total return yielded by a bond until its maturity. The formula for calculating YTM is [(face values/present value) ^1/time period]-1
- In this scenario, the bond price is $900 and yields $20 dollars annually. Therefore, the YTM is 20/900= 0.0222
When rounded off, the value equals a yield of 2.2%
- The price is $950, the face value of $,1,000 and 1 years of maturity
Calculation: (1,000/950) ^ (1/1)-1= 0.05263
This value can be rounded and listed as a yield of 5.26%.
- The bond has a price and face value of $950 and $ 1,000, respectively. The bond is also expected to mature after 2 years.
Calculation: (1,000/950) ^ (1/2)-1= 0.025978
This value can be rounded and listed as a yield of 2.6%
- The bond has a price of $890, a face value of $1,000, a coupon rate of 5%, and 10 years to maturity.
Calculation:
YTM= Annual interest + {[par value- market price]}/ {Par value+ market price}/2
If the coupon rate is 5%, the annual coupon is $50 (5%*1000)
YTM= $50+ [($1,000-$890)/5]/ ($1,000+$890)/2
Answer= 0.0768
This value can be rounded and listed as a yield of 7.68%
Question Three
- In scenario 1, the bond’s coupon rate is 10%, with a 10-year maturity and $1000 face value. If the interest rate falls next year from 10% to 7%, then the bond price is $700 (7%*1000/10%). This value implies that after one year, the bondholder will sell it for $700 after purchasing it for $1,000.
Step One: Calculate the bonds return after one year
n= 1 year
Interest rate=10% (0.01)
Bond return: 1.01^1= 1.01
1.01*700= $707
Subtract the principal from the bond’s selling price: $707-$700= $7
This value suggests that the bondholder will profit or have a capital gain of $7 from the bond’s returns.
Calculate the holding period return:
The value can be calculated by subtracting the bond return from the face value. Therefore, the holding period return in this scenario is $293 ($1000-707).
- The bond price in scenario 2 has a current price of $500 and pays $50 annually till infinity. The bond’s interest rate falls from 10% to 7%, implying that the selling price is $350.
Calculate the bond’s price after one year
n=1 year
interest rate= 10% (0.01)
Bond return: 1.01^1= 1.01
1.01*350=$353.50
Subtract the principal from the bond’s selling price: $353.50-$350=
This value suggests that a capital gain of $3.50 will be obtained from the bond.
Calculate the holding period return: $500-$353.50= $146.5
- In this scenario, the T-bill is selling for $1502.63, matures in 3 years, and has a face value of $2000. If the interest rate falls from 10% to 7%, it will sell for $1051.84
Calculate the T-bill price after one year
n=1 year
interest rate= 10% (0.01)
T-bill return: 1.0161= 1.01
1.01*1051.84= $1062.36
Subtract the principal from the T-bill’s selling price: $1062.36- $1051.84= $10.52
The capital gain for the T-bill is $10.52
The holding period is $1502.63-$1062.36= $440.27
In my view, I would prefer to hold the Government of Canada T-bill because it has a shorter maturity period, implying that it would have fewer coupon payments after the fall in interest rates.
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