1.Sasha owns two investments, A and B, that have a combined total value of 48,70
ID: 2814069 • Letter: 1
Question
1.Sasha owns two investments, A and B, that have a combined total value of 48,700 dollars. Investment A is expected to pay 21,100 dollars in 1 year(s) from today and has an expected return of 6.55 percent per year. Investment B is expected to pay 45,370 dollars in T years from today and has an expected return of 6.88 percent per year. What is T, the number of years from today that investment B is expected to pay 45,370 dollars? Round your answer to 2 decimal places (for example, 2.89, 14.70, or 6.00).
2.3 year(s) ago, Fatima invested 6,170 dollars. In 1 year(s) from today, she expects to have 7,870 dollars. If Fatima expects to earn the same annual return after 1 year(s) from today as the annual rate implied from the past and expected values given in the problem, then in how many years from today does she expect to have exactly 12,210 dollars? Round your answer to 2 decimal places (for example, 2.89, 14.70, or 6.00).
Explanation / Answer
1)
Present value of A = 21100 / 1.0655 = 19802.91
Present value of B = 48700 - 19802.91 = 28897.09
28897.09 = 45370 / 1.0688T
1.0688T = 45370 / 28897.09 = 1.57
T = ln(1.57) / ln(1.0688)
= 6.78 years
2)
(1+r)4 = 7870 / 6170 = 1.28
r = 1.281/4 - 1 = 6.27%
Current investment value = 6170*(1+6.27%)3 = 7405.47
Years = ln(12210/7405.47) / ln(1.0627)
= 8.22 years
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