A perpetuity pays 1 at the end of every year plus an additional 1 at the end of every second year. The present value of the perpetuity is K for i > 0.

Determine K.

• [[math]]\frac{i+3}{i(i+2)}[[/math]]
• [[math]]\frac{i+2}{i(i+1)}[[/math]]
• [[math]]\frac{i+1}{i^2}[[/math]]
• [[math]]\frac{3}{2 i}[[/math]]
• [[math]]\frac{i+1}{i(i+2)}[[/math]]

References

Hlynka, Myron. "University of Windsor Old Tests 62-392 Theory of Interest". web2.uwindsor.ca. Retrieved November 23, 2023.

Deposits are to be made to a fund each January 1 and July 1 for the years 1995 through 2005. The deposit made on each July 1 will be 10.25% greater than the one made on the immediately preceding January 1. The deposit made on each January 1 (except for January 1, 1995) will be the same amount as the deposit made on the immediately preceding July 1. The fund will be credited with interest at a nominal annual rate of 10%, compounded semi-annually. On December 31, 2005, the fund will have a balance of 11000.

Determine the initial deposit to the fund.

• 160
• 165
• 175
• 195
• 200

References

Hlynka, Myron. "University of Windsor Old Tests 62-392 Theory of Interest". web2.uwindsor.ca. Retrieved November 23, 2023.

At an annual effective interest rate of i, i > 0, both of the following annuities have a present value of X:

1. a 20-year annuity-immediate with annual payments of 55
2. a 30-year annuity-immediate with annual payments that pays 30 per year for the first 10 years, 60 per year for the second 10 years, and 90 per year for the final 10 years.

Calculate X.

• 575
• 585
• 595
• 605
• 615

References

Hlynka, Myron. "University of Windsor Old Tests 62-392 Theory of Interest". web2.uwindsor.ca. Retrieved November 23, 2023.

For a given positive integer [math]n[/math], a rate of interest [math]i[/math] can be found for which [math]4 a_{\overline{2 n} \mid i}=5 a_{\overline{n} \mid i}[/math].

Express in terms of [math]n[/math] how long it will take for money to double at this rate of interest.

• [math]\sqrt{n}[/math]
• [math]n/2[/math]
• [math]5n/8[/math]
• [math]n/\sqrt{2}[/math]
• [math]2n[/math]

References

Hlynka, Myron. "University of Windsor Old Tests 62-392 Theory of Interest". web2.uwindsor.ca. Retrieved November 23, 2023.

An annuity immediate pays an initial benefit of 1 per year, increasing by 10.25% every four years. The annuity is payable for 40 years. Using an annual effective rate of 5%, find the present value of this annuity.

• 21.5
• 22.3
• 23.8
• 24.1
• 24.6

References

Hlynka, Myron. "University of Windsor Old Tests 62-392 Theory of Interest". web2.uwindsor.ca. Retrieved November 23, 2023.

An annual perpetuity immediate is divided among four charities W,X,Y,Z. W is to receive the first n annual payments, X the next n, Y the third n, and Z the rest. Denote W’s share by w, X’s share by x, Y’s share by y, Z’s share by z. If w − 2x = z − y, evaluate w/z.

• 1/2
• 1
• 2
• 4
• 8

References

Hlynka, Myron. "University of Windsor Old Tests 62-392 Theory of Interest". web2.uwindsor.ca. Retrieved November 23, 2023.

Find the present value of a perpetuity with payments every two years beginning immediately where the payments have the form p, p + q, p + 2q, p + 3q, . . .

References

Hlynka, Myron. "University of Windsor Old Tests 62-392 Theory of Interest". web2.uwindsor.ca. Retrieved November 23, 2023.

Mary purchases an increasing annuity-immediate for 50,000 that makes twenty annual payments as follows:

1. P, 2P, . . . , 10P in years 1 through 10, and
2. 10P (1.05), 10P (1.05)², . . . , 10P (1.05)¹⁰ in years 11 through 20.

The annual effective interest rate is 7% for the first 10 years and 5% thereafter.

Calculate P

• 564,
• 574
• 584
• 594
• 604

References

Hlynka, Myron. "University of Windsor Old Tests 62-392 Theory of Interest". web2.uwindsor.ca. Retrieved November 23, 2023.

Suppose you invest $10,000 per year for 10 years at an average return of 5.5%. The average future inflation rate is 2% per year.

Determine the purchasing power, in today's dollars, of your investments.

• $105,623
• $111, 432
• $135, 835
• $140,253
• $142,111

References

Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 20, 2023.

Your sales are $10 million this year and expected to grow at 5% in real terms for the next three years. The appropriate nominal discount rate is 10%. The inflation is expected to be 2% per year during the same period. What is the present value of your sales revenue for the next three years?

• $19.22M
• $24.87M
• $27.23M
• $28.45M
• $29.2M

References

Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.