Money accumulates in a fund at an effective annual interest rate of i during the first three years and at an effective annual interest rate of 3i thereafter. A deposit of 100 is made into a fund at time 0. It accumulates to 178.66 at the end of 10 years and to 368.21 at the end of 20 years.

What is the value of the fund at the end of 8 years?

• 122
• 135
• 155
• 162
• 178

References

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

Solution: C

[[math]] 368.21=178.66(1+3 i)^{10} \text { so } 1+3 i=(368.21 / 178.66)^{\cdot 1}=1.074996 [[/math]]

Thus [math]i=.074996 / 3=.024999[/math]. Value after 8 years is [math]\left.100(1+i)^3(1+3 i)^5=100(1.024999)^3\right)(1.074996)^5=154.60[/math].

References

Hlynka, Myron. "University of Windsor Old Tests 62-392 Theory of Interest". web2.uwindsor.ca. Retrieved November 23, 2023. Thus [math]i=.074996 / 3=.024999[/math]. Value after 8 years is [math]\left.100(1+i)^3(1+3 i)^5=100(1.024999)^3\right)(1.074996)^5=154.60[/math].