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14 Jack and Jill are twins. Jack invested $1,000, earned 9% annually, and now has $1,992.56. Jill invested $1,000, earned 6.47%, and now has $1,992.97. Jack invested his money years ago. 12 (B) 11 (C) 10 (D) 9 (E) 8

User Fdorssers
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3 votes

Answer:

(E) 8

Explanation:

We can determine how many years ago Jack invested his money using the lump sum future value formula, which is given by:

FV = PV * (1 + r)^n, where

  • FV is the future value,
  • PV is the present value,
  • r is the rate (the percentage is converted to a decimal)
  • and n is the time in years.

Since we already know that the future value is $1992.56, the present value is $1000, the rate is 0.09, we can now solve for n, the time in years using the following steps:

Step 1: Plug 1992.56 for FV, 1000 for PV, 0.09 for r and simplify on the right-hand side;

1992.56 = 1000(1 + 0.09)^n

1992.56 = 1000(1.09)^n

Step 2: Divide both sides by 1000:

1992.56 = 1000(1.09)^n) / 1000

1.99256 = 1.09^n

Step 3: Take the logs of both sides and bring down n on the right-hand side:

log (1.99256) = log (1.09^n)

log (1.99256) = n * log (1.09)

Step 4: Divide both sides by log (1.09) and round to the nearest whole number:

log (1.99256) / log (1.09) = n

7.999984616 = n

8 = n

Thus, Jack invested his money about 8 years ago so the answer is (E)

User Abhishek Sagar
by
7.9k points
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