Jeff deposits 10 into a fund today and 20 fifteen years later. Interest is credited at a nominal discount rate of d compounded quarterly for the first 10 years, and at a nominal interest rate of 6% compounded semiannually thereafter. The accumulated balance in the fund at the end of 30 years is 100.

• 4.33%
• 4.43%
• 4.53%
• 4.63%
• 4.73%

Calculate d.

References

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

On July 1, 1999, a person invested 1000 in a fund for which the force of interest at time [math]t[/math] is given by [math]\delta_t=\frac{3+2 t}{50}[/math], where [math]t[/math] is the number of years since January 1, 1999. Determine the accumulated value of the investment on January 1, 2000.

• 1036
• 1041
• 1045
• 1046
• 1051

References

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

At a nominal interest rate of i convertible semi-annually, an investment of 1000 immediately and 1500 at the end of the first year will accumulate to 2600 at the end of the second year.

Calculate i.

• 2.75%
• 2.77%
• 2.79%
• 2.81%
• 2.83%

References

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

You are given that [math]a(t)=K t^2+L t+M[/math], for [math]0 \leq t \leq 2[/math], and that [math]a(0)=100, a(1)=110[/math], and [math]a(2)=136[/math].

Determine the force of interest at time [math]t=1 / 2[/math].

• .030
• .049
• .061
• .095
• .097

References

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

The present value of 200 paid at the end of [math]n[/math] years, plus the present value of 100 paid at the end of [math]2 n[/math] years is 200 .

Determine the annual effective rate of interest.

• [[math]]\left(\frac{\sqrt{3}+1}{2}\right)^{1 / n}-1[[/math]]
• [[math]]1-\left(\frac{\sqrt{3}-1}{2}\right)^{1 / n}[[/math]]
• [[math]]\left(\frac{\sqrt{3}-1}{2}\right)^{1 / n}-1[[/math]]
• [[math]]\left(\frac{\sqrt{3}+1}{2}\right)-1[[/math]]
• [[math]]1-\left(\frac{\sqrt{3}-1}{2}\right)^{1/ 2 n}[[/math]]

References

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

Jennifer deposits 1000 into an account. Interest is credited at a nominal annual rate of i convertible seminannually for the first 7 years and at rate 2i convertible quarterly for the all years thereafter. The accumulated amount after 5 years is X. The accumulated amount at the end of 10.5 years is 1980.

Calculate X.

• 1200
• 1225
• 1250
• 1275
• 1300

References

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

A deposit of 100 is made into a fund at time [math]t=0[/math]. The fund pays interest at a nominal annual rate of discount [math]d[/math] compounded quarterly for the first two years. Beginning at time [math]t=2[/math], interest is credited at a force of interest [math]\delta_t=\frac{1}{t+1}[/math]. At time [math]t=5[/math], the accumulated value of the fund is 260. Calculate [math]d[/math].

• 12.7%
• 12.9%
• 13.1%
• 13.3%
• 13.5%

References

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

Fund A accumulates at rate [math]12 \%[/math] convertible monthly. Fund [math]\mathrm{B}[/math] accumulates with force of interest [math]\delta_t=t / 6[/math], in years. At time zero, 1 is deposited into each fund. Let [math]T[/math] be the time when the two funds are equal.

Determine [math]T[/math], in years.

• [math]12 \ln (1.01)[/math]
• [math]12 \ln (1.12)-\ln (1.01)[/math]
• [math] 12 \ln (1.12)[/math]
• [math]144 \ln (1.01)[/math]
• [math]144\ln(1.12)[/math]

References

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

Find the first derivative with respect to [math]i[/math] of [math]f(i)=\frac{\delta}{d}[/math].

• 0
• [math]\frac{i-\delta}{i^2}[/math]
• [math]\frac{d^2}{i^2}\left(1-\frac{i}{\delta}\right)[/math]
• [math]\frac{\delta-i}{i^2}[/math]
• [math]\frac{d^2}{i^2}\left(\frac{i}{\delta}-1\right)[/math]

References

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

A fund earns interest at a rate equivalent to 5% per annum effective. A person makes continuous deposits to the Fund for 10 years The rate at which deposits are made is 1000+100t per annum at time t (in years). How much will the person have in the fund at the end of the ten year period. (Set up the proper integral but do not evaluate. The letters i, v, δ should not appear in your integral.)

• [[math]]\int_0^{10}(1000+100 t)e^{10-t} d t [[/math]]
• [[math]] \int_0^{10}(1000+100 t)\left(1.05^{t}\right) d t [[/math]]
• [[math]]1.05^{10} \int_0^{10}\exp{(1000+100 t)\left(1.05^{-t}\right)} d t [[/math]]
• [[math]]1.05^{10} \int_0^{10}(1000+100 t)\left(1.05^{t}\right) d t [[/math]]
• [[math]]1.05^{10} \int_0^{10}(1000+100 t)\left(1.05^{-t}\right) d t [[/math]]

References

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