For an earlier post Economics in the Rear-view Mirror transcribed the examination questions for George Heberton Evans’ course on corporation finance offered to Johns Hopkins undergraduates in 1937-1938. That course and the following course on the mathematics of finance and applied statistics were not listed as prerequisites for each other. The essential difference appears to be that the following course appears to have covered themes of interest to actuaries (no pun intended).
For some background information about Evans, see: Ph.D. from Johns Hopkins University, 1925.
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Course Description
Mathematics of Finance and Applied Statistics
1937-1938
24 B. Mathematics of Finance and Applied Statistics. Associate Professor Evans. Three hours weekly through the year. F., S., 11.30. Gilman Hall 314.
The first half-year of the course will include the study of annuities, sinking funds, amortization tables, and valuation of bonds.
During the second half-year mathematics and statistical method will be applied to business and economic problems.
Prerequisites: Mathematics 1 C or 2 C and Political Economy 2 C.
Source: The Johns Hopkins University Circular (1937).
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Semester Examinations for
Mathematics of Finance and Applied Statistics
1937-1938
THE JOHNS HOPKINS UNIVERSITY
MID-YEAR EXAMINATION
POLITICAL ECONOMY 24 B
Dr. Evans
February 4, 1938
1 p.m.
- A bond will be redeemed in 10 years for $1,000 cash. Semi-annually the owner of the bond receives $30 interest. Determine the present value of the bond if the current rate on similar investments is 5%.
- Find the bank discount on a $10,000 note for 6 months when the bank rate is 7%. What is the effective rate of interest charged!
- The XYZ Corporation has outstanding a bond issue of $10,000. It has agreed to pay to a trustee an amount at the end of each year, which invested at 4% will provide a fund to retire these bonds at the end of 10 years. Determine the amount that must be invested each year.
- Williams owes $7,500 due in 8 years, and $4,500 due in 5 years, each bearing 4% interest. What two equal payments will liquidate this debt, if the first is made in 1 year, and the second in 3 years? The current rate is 5%.
- Repairs costing $350 must be made each 2 years to a building which will last 20 years. Determine the amount that could be spent to eliminate these repairs without additional cost to the owner over the period. Interest at 4%.
- An estate left 110 years ago was unclaimed until recently. An heir has proved his claim and is to receive the estate of $50,000 with interest at 3% annually for 110 years. Determine the value of the estate.
- X has an obligation of $25,000 which he desires to liquidate by investing $3,500 now and the same sum annually thereafter, at 4½% compounded semi-annually. Determine when the fund should theoretically be large enough to liquidate the debt.
- Find the ordinary interest of $450 for 60 days at 8%.
- An insurance company agrees to pay you or your estate $2,000 a year for 15 years if you will pay them $23,875.87 cash. The salesman argues that you will get your money back and make a profit of $6,124.13. Determine the rate of interest that you will actually receive.
- In order to attract customers the Pacific Savings Bank advertises that it pays 3% compounded monthly. If you deposit $25 a month for 6 years what is the amount you will have accumulated at the end of 6 years?
- In how many years will money invested at compound interest double itself at 3%?
- In 10 years the bond issue of the Chemico Company will mature. An amount of $30,000 will be needed to retire this issue. The treasurer estimates that $2,300 a year will be available for investment. What rate of interest must be earned to accumulate a fund of $30,000 in 10 years? In answering, make use of the binomial theorem.
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THE JOHNS HOPKINS UNIVERSITY
FINAL EXAMINATION
POLITICAL ECONOMY 24 B
June 4, 1938
- A bequest of $150,000 was left to A, aged 36. With what life annuity will this provide him?
- A, aged 40, gave $75,000 to Blank University with the understanding that after 15 years he receive an equivalent life annuity. What annual amount would he receive?
- A party of five men at a soda fountain match coins, agreeing that the odd man is to pay for the drinks: (a) What is the probability that there will be one odd man at the first attempt? (b) What is the probability that there will be no odd man at the first attempt, but that there will be one on the second? (c) What is the probability that there be an odd man at least once in two attempts?
- What is the earliest age at which the “odds are against” a man living:
(a) one year?
(b) five years? - Using the theoretical method, calculate the purchase price of the following $1000 bond which was bought on May 4, 1928 to yield 4.40%: New England Tel. & Tel. 5’s, due Oct. 1, 1932, with coupon dates of Apr. 1 and Oct. 1.
- Dwight Minor paid, at the end of each month, dues of $23.25 on his 31 shares of $100 par value stock in the Garfield Loan and Savings Association. Immediately after his 99th payment the stock matured. What approximate rate, converted monthly, did his association allow him?
- B, aged 36, took out a 20-year endowment insurance policy for $50,000 to be paid for in 20 payments. On what net annual premium did the insurance company base its charge?
Source: Johns Hopkins University, Eisenhower Library. Ferdinand Hamburger, Jr. Archives. Department of Political Economy. Curricular Materials. Series 6. Box 2. Folder “Department of Political Economy — Exams, 1936-1940”.
Image Source: Johns Hopkins University, Sheridan Libraries, Graphic and Pictorial Collection. George Heberton Evans at approximately 40 years old. The portrait was colorized by Economics in the Rear-view Mirror.