On January 1, 2003, Jack invested $5,000 at r percent interest rate

On January 1, 2003, Jack invested $5,000 at r percent interest rate, compounded annually. What is the value of r?
P = 5000, Rate, r = ?
Amount at the end of 2003, \(A_{2003} = P*(1+\frac{r}{100}) = 5000(1+\frac{r}{100})\)

(1) The investment plus the total interest at the end of 2004 was $550 more than the amount at the end of 2003.
\(A_{2004} - A_{2003} = 5000*(1+\frac{r}{100})^2 - 5000(1+\frac{r}{100}) = 550\)
\(5000*x^2 - 5000x = 550\)
'x' and r an be solved.

SUFFICIENT.

(2) The investment plus the total interest at the end of 2004 increased by 21% from the original investment.
Here 21% can be treated as simple interest, compounded annually only once or once in two years
\(A_{2004} = 5000*(1+\frac{21}{100})\)
\(5000*(1+\frac{21}{100}) = 5000*(1+\frac{r}{100})^2\)
'r' can be calculated.

SUFFICIENT.


Answer D.