Weekly tests Finance
Week 1
1. You expect to receive USD 5,500 in exactly one year. The annual interest rate is
2.0%. The present value of the receipt is
5500/ 1.02^1 = 5392
2. You expect to receive GBP 2,500 in exactly 8 years. The interest rate is 3.2% per
year. The present value of this receipt is
1
.032 ^8 = 1943
3. You deposit EUR 5,700 at a bank that offers 4.9% interest on deposits for one
year. The value of your deposit after one year is
5700 x 1.049 = 5979
4. You deposit EUR 5,800 at a bank that offers 4.4% interest on deposits for one
year. The value of your deposit after one year is
5800 x 1.044 = 6055
5. An investment of EUR 720 will generate a future cash flow of EUR 700. The
market price of a similar asset is EUR 690. The net present value of the
investment is
-30
Want -20 op de cash flow en -10 in general.
6. An investment of USD 210 will generate a future cash flow of USD 110. The
market price of a similar asset is USD 270. Is this an attractive investment
opportunity?
Yes, since the net present value of the investment is positive
7. You expect to receive GBP 10,400 in exactly one year, and GBP 8,500 in exactly
two years. The annual interest rate is 2.5%. The present value of these receipts
is
/.025 = 10.146
.025 ^2 = 8090
10.146 + 8090 = 18.237
8. You expect that next year's cash flow will be EUR 700 and that this cash flow will
grow with 2.9% forever. The interest rate is 14.0%. Today's value of this stream
0.43*5.58/(0.099 - (1 -
of cash flows is 0.43)*0.111) = EUR 67.15
700 / (14-2.9) = 6306
9. A liability requires 12 annual payments of USD 920 starting one year from now.
The interest rate is 5.9%. The present value of this liability is
Also this formula with quarterly payments!
PV = FV / (1+ interest)
.059 = ..
.. /1.059 = … Dat 12 keer = 7756
,10. You invest $10,000 at an annual interest rate of 2.6%. Your investment doubles
in
10000 * 1.026 =..
Op = blijven drukken en tellen hoe vaak je gedrukt hebt tot er 20.000 staat.
27 years
11. You deposit for 11 years each year USD 590 into a savings account. The savings
account has an interest rate of 2.7% per year. The balance of your savings
account just after the last deposit is
Year 1 =590
1
Year 2 = 590 x 1.027 +590
Etc. etc.
Year 11 = 7441
12. You expect that next year's cash flow will be EUR 340, and that this cash flow will
grow with 4.0% forever. The market price of this stream of cash flows is EUR
5,054. The expected return of an investment in these cash flows is
() x 100 = 6.727
6.727 + 4 = 10.73%.
10.73%
13. A loan of EUR 70,000 is amortized with equal annual payments in 13 years. The
first payment is in exactly one year. The interest rate on the loan is 2.2%. The
annual payment is
Annuity formula
C * (1-1/(1+r)^n) / r
C * (1 – 1/(1+0,022)^13) / 0,022 = 70.000
C * 0,,022 = 70.000
C * 11,182 = 70.000
70.,182 = 6250
Formule in de sheet kan ook met quarterly!!
A loan of 6000 is repaid with equal quarterly payments in 12 quarters. The first
payment is in exactly one quarter. The equivalent interest rate on the loan is
0,8%. The quarterly payment is 526,38
14. A liability requires 5 annual payments of USD 200. The interest rate is 2.7%. The
present value of this liability just before the first payment is
C * (1-1/(1+r)^n) / r 0.43*5.58/(0.099 - (1 -
200 * (1-1/(1+0,027)^5) / 0,027 0.43)*0.111) = EUR 67.15
200 * 0,,027 = 923,8
923,8 x 1,027 = 949
When it says just before, you multiple it with 1+%
,Week 2
1. A loan has a stated annual percentage rate of 4.7% with monthly
compounding. The equivalent annual interest rate of this loan is
EAR = ((1 + 0.047/12)^12) – 1 = 4.80%
2. You expect to receive GBP 49,000 in exactly one year, and GBP 62,000 in
exactly two years. The yield to maturity of one-year zero-coupon bonds is
6.0%, and the yield to maturity of two-year zero-coupon bonds is 7.6%.
Today's value of these receipts is
49000/ 1.06 = 46226
62000/1.076^2 = 53550
2
46226 + 53550 = 99777
3. You expect to receive USD 21.1 million after 7 months, the equivalent annual
interest rate is 3.0%. Today's value of this receipt is
FV/ (1 + r ) ^n
N is in dit geval 7 maanden, dus 7/12 = 0.58.
21.1 / (1+ 3%) ^ 0.58 = 20.74 million
4. The equivalent annual interest rate is 3.3%. The equivalent discount rate for
monthly cash flows is
0.033 +1 ^(1/12) -1 x100 = 0.2709
5. You deposit EUR 2,400 at a savings account with an annual percentage rate
of 3.24% with quarterly compounding. The balance of your savings account
after 13 quarters is
2400 x ( 1 + 0.0324/4) ^ 13 = 2665.37
6. You deposit for 11 months, each month GBP 1,230 into a savings account.
The saving account has an annual percentage rate of 1.92% with monthly
compounding. The balance of your savings account just after the last deposit
is
1. = 0.16 = 0.0016
1230/0.0016 x ((1+0.0016)^11 -1) = 13639
7. A loan of GBP 70,000 with an annual percentage rate of 3.36% with monthly
compounding is amortized with equal monthly payments in 3 years. The first
payment is in 1 month. The monthly payment is
70000 x (0.0336/12)
------------------------
(1-(1+(0.0336/12))^-12*3) = 2046.81 0.43*5.58/(0.099 - (1 -
0.43)*0.111) = EUR 67.15
8. You expect to receive GBP 50,000 in exactly one year, and GBP 40,000 in
exactly two years. The one-year spot rate is 3.9%, and two-year spot rate is
4.2%. Today's value of these receipts is
50000 x (100-3.9)=
40000 x (100-4.2)^2 =
84761
, 9. A zero-coupon bond has a face value of USD 1,000, a remaining maturity of 9
years, and a market price of USD 917.11. The yield to maturity of this bond is
.11 ^ (1/9) = 1.00966
1.00966 -1 = 0.00966
0.00966 x 100 = 0.97%
10. A zero-coupon bond has a face value of EUR 1,000 and a remaining maturity
of 3.6 years. The yield to maturity of comparable bonds is 1.44%. The price of
this bond is
1000 / (1+0.0144)^3.6 = 949.83
11. A coupon bond with a face value of USD 1,000 has an annual coupon of
2
3.5%, and a remaining maturity of 11 years. The yield to maturity of
comparable bonds is 1.2%. The price of this coupon bond is
35/0.012 x ( 1- 1.012^-11)+ 1000 x 1.012^-11 = 1,236
A bond with a face value of $1,000 has an annual coupon of 6% and a remaining
maturity of 12 years. The yield to maturity of comparable bonds is 3%. The value of
this bond is
Answer
C. $1,299.
60/0,03 x (1-1.03^-12)+(1000x(1.03^-12)) = 1298,6
12. A coupon bond with a face value of EUR 1,000 has an annual coupon of 4.7%
and a remaining maturity of 2 years. The yield to maturity of one-year zero-
coupon bonds is 4.92% and the yield to maturity of two-year zero-coupon
bonds is 5.15%. The price of this bond is
47/1.0492 + 1047/1.0515^2 = 992
13. A coupon bond with a face value of USD 1,000 has an annual coupon of
2.0%, and a remaining maturity of 13.5 years. The yield to maturity of
comparable bonds is 1.1%. The price of this bond is
20/0.011 x (1-1.011^ -13.5) + 1000 x1.011^-13.5 = 1112
??
14. A coupon bond with a face value of EUR 1,000 has a coupon of 3.8%, semi-
annual coupon payments, and a remaining maturity of 8 years. The yield to
maturity of comparable bonds is 2.9%. The price of this bond is 1063,85 - (1 -
0.43*5.58/(0.099
0.43)*0.111) = EUR 67.15
A bond with a face value of $1,000 has an annual coupon of 3% and a
remaining maturity of 5 years; the yield to maturity of comparable bonds is
2.0%. The value of this bond is calculated as
