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Clara made two investments. Investment A has an initial value of $500 and

increases by $45 every year. Investment B has an initial value of $300 and
increases by 10% every year. Clara checks the value of her investments once a
year, at the end of the year. What is the first year in which Clara sees that
Investment B's value has exceeded investment A's value?

User Dooleyo
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1 Answer

3 votes

Answer:

The first year in which Clara will see that Investment B's value will exceed Investment A's value will be year 14.

Explanation:

Since Clara made two investments, and Investment A has an initial value of $ 500 and increases by $ 45 every year, while Investment B has an initial value of $ 300 and increases by 10% every year, and Clara checks the value of her investments once to year, at the end of the year, to determine what is the first year in which Clara sees that Investment B's value has exceeded investment A's value, the following calculation must be performed:

500 + (45 x X) = A

300 x 1.1 ^ X = B

A = 500 + 45 x 5 = 500 + 225 = 725

B = 300 x 1.1 ^ 5 = 483.15

A = 500 + 45 x 10 = 950

B = 300 x 1.1 ^ 10 = 778.12

A = 500 + 45 x 15 = 1175

B = 300 x 1.1 ^ 15 = 1253.17

A = 500 + 45 x 14 = 1,130

B = 300 x 1.1 ^ 14 = 1,139.25

Therefore, the first year in which Clara will see that Investment B's value will exceed Investment A's value will be year 14.

User Martin Gardener
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