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)