Question

2 year(s) ago, Omar had 102,000 dollars in his account. In 5 year(s), he expects to have 317,700 dollars. If he has earned and expects to earn the same return each year from 2 year(s) ago to 5 year(s) from today, then how much does he expect to have in 3 year(s) from today?

1 year(s) ago, Fatima invested 6,430 dollars. In 1 year(s) from today, she expects to have 7,960 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 10,190 dollars? Round your answer to 2 decimal places (for example, 2.89, 14.70, or 6.00).

Answer 1

1. Number of Years of Investment by Omar = 7 years
Rate = (317,600/102,200)^1/7 -1 = 17.58%

FV of Investment 3 years from today = 102,000*(1+17.58%)⁵ = 229,263.86

2. Number of years invested by Fatima = 2
Rate = (7960/6430)^1/2 -1 = 11.26%
Let number of years from today = n-1
10190 = 6430*(1+11.26%)ⁿ
10190/6430 = 1.1126ⁿ
Applying log on both sides we get
n = Log (10190/6430)/log(1.1126) = 4.32
So number of years from today = 4.32-1 = 3.32/

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