Eric made two investments: Investment Q QQ has a value of $ 5 0 0 $500dollar sign, 500 at the end of the first year and increases by $ 4 5 $45dollar sign, 45 per year. Investment R RR has a value of $ 4 0 0 $400dollar sign, 400 at the end of the first year and increases by 1 0 % 10%10, percent per year. Eric checks the value of his investments once a year, at the end of the year. What is the first year in which Eric sees that investment R RR's value exceeded investment Q QQ's value?
Answers
Given: Eric made two investments: Q has a value of $500 & R has a value of $400
To find : first year in which Eric sees that investment R value exceeded investment Q value?
Solution:
Let say after n years Eric sees that investment R value exceeded investment Q value
Q Value = 500 $
Q value after n Years = 500 + 45n
R value = 400 $
R value after n year = 400 ( 1 + 10/100)ⁿ
400 ( 1 + 10/100)ⁿ > 500 + 45n
= 400 ( 1.1)ⁿ > 500 + 45n
n = 8
400 ( 1.1)⁸ = 857
500 + 45* 8 = 860
n = 9
400 ( 1.1)⁹ = 943
500 + 45* 9 = 905
=> after 9 Years Eric sees that investment R value exceeded investment Q value
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Answer:
10. It's on khan academy.