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07 Aug 2026, 05:31
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A school sets aside $1,860 to be divided among three students: Arman, Bela, and Cora. Each student’s share will be deposited at 10% annual simple interest. Arman’s share will be deposited for 2 years, Bela’s share for 4 years, and Cora’s share for 5 years. If the shares are chosen so that the three deposits have the same value at the end of their respective deposit periods, how much is Cora’s original share?
A. $520
B. $540
C. $560
D. $600
E. $620
A. $520
B. $540
C. $560
D. $600
E. $620
07 Aug 2026, 05:31
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Official Solution:
A school sets aside $1,860 to be divided among three students: Arman, Bela, and Cora. Each student’s share will be deposited at 10% annual simple interest. Arman’s share will be deposited for 2 years, Bela’s share for 4 years, and Cora’s share for 5 years. If the shares are chosen so that the three deposits have the same value at the end of their respective deposit periods, how much is Cora’s original share?
A. $520
B. $540
C. $560
D. $600
E. $620
Let the common final value of each deposit be \(F\).
At simple interest, final value \(=\) principal \(* (1 + rt)\), where \(r\) is the annual interest rate as a decimal and \(t\) is the number of years.
• Arman’s share is deposited for 2 years, so his deposit grows by a factor of \(1 + 0.10 * 2 = 1.2 = \frac{6}{5}\).
So Arman’s original share is \(\frac{F}{6/5} = \frac{5F}{6}\).
• Bela’s share is deposited for 4 years, so her deposit grows by a factor of \(1 + 0.10 * 4 = 1.4 = \frac{7}{5}\).
So Bela’s original share is \(\frac{F}{7/5} = \frac{5F}{7}\).
• Cora’s share is deposited for 5 years, so her deposit grows by a factor of \(1 + 0.10 * 5 = 1.5 = \frac{3}{2}\).
So Cora’s original share is \(\frac{F}{3/2} = \frac{2F}{3}\).
Since the total original amount is $1,860:
\(\frac{5F}{6} + \frac{5F}{7} + \frac{2F}{3} = 1,860\)
\(\frac{35F}{42} + \frac{30F}{42} + \frac{28F}{42} = 1,860\)
\(\frac{93F}{42} = 1,860\)
\(F = 840\)
Cora’s original share is:
\(\frac{2}{3} * F = \frac{2}{3} * 840 = 560\)
Answer: C
A school sets aside $1,860 to be divided among three students: Arman, Bela, and Cora. Each student’s share will be deposited at 10% annual simple interest. Arman’s share will be deposited for 2 years, Bela’s share for 4 years, and Cora’s share for 5 years. If the shares are chosen so that the three deposits have the same value at the end of their respective deposit periods, how much is Cora’s original share?
A. $520
B. $540
C. $560
D. $600
E. $620
Let the common final value of each deposit be \(F\).
At simple interest, final value \(=\) principal \(* (1 + rt)\), where \(r\) is the annual interest rate as a decimal and \(t\) is the number of years.
• Arman’s share is deposited for 2 years, so his deposit grows by a factor of \(1 + 0.10 * 2 = 1.2 = \frac{6}{5}\).
So Arman’s original share is \(\frac{F}{6/5} = \frac{5F}{6}\).
• Bela’s share is deposited for 4 years, so her deposit grows by a factor of \(1 + 0.10 * 4 = 1.4 = \frac{7}{5}\).
So Bela’s original share is \(\frac{F}{7/5} = \frac{5F}{7}\).
• Cora’s share is deposited for 5 years, so her deposit grows by a factor of \(1 + 0.10 * 5 = 1.5 = \frac{3}{2}\).
So Cora’s original share is \(\frac{F}{3/2} = \frac{2F}{3}\).
Since the total original amount is $1,860:
\(\frac{5F}{6} + \frac{5F}{7} + \frac{2F}{3} = 1,860\)
\(\frac{35F}{42} + \frac{30F}{42} + \frac{28F}{42} = 1,860\)
\(\frac{93F}{42} = 1,860\)
\(F = 840\)
Cora’s original share is:
\(\frac{2}{3} * F = \frac{2}{3} * 840 = 560\)
Answer: C
