A person deposits 100 at the beginning of each year for 20 years. Simple interest at a rate of i per year grows the account to 2840 at the end of 20 years. If compound interest at the same rate i had been used, what would be the accumulated value in the account after 20 years?

• 2890
• 3100
• 3200
• 3310
• 3470

References

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

Solution: B

[[math]] 2840=100(1+20 i)+100(1+19 i)+\cdots+100(1+i)=2000+i * 100(21)(20) / 2 \text { so } i=16.80 / 420=.04 [[/math]]

Using compound interest, accumulated amount is

[[math]] 100 \ddot{s}_{\overline{20} \mid .04}=100 \frac{1.04^{21}-1.04}{.04}=3096.92 [[/math]]

References

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