Shouldn't the PV equal PV = C(1/e^r - (1/e^r)*(1/e^r*t)?

(C) The present value of a continuous stream of cash flows, amounting to $2,000 per year, starting immediately and continuing for 15 years The continuous stream of cash flows is $2,000. The time periodumber of years is 15. The continuous compounding interest rate is 12%. Calculate the present value as follows: Present value=Cash flow stream x Interest rate x time Interest rate Interest rate 1 = $2,000 x 12%x15 12% 12% 2.71828182845905 1 1 12% 12% 2.71828182845905" = $2,000 x X 180% 1 = $2,000 12% 12% 6.04964746441294 8.33333333333333 = $2,000 x -8.33333333333333 x 0.165298888221587 = $2,000 (8.33333333333333 - 1.37749073517989) = $2,000 (6.95584259815345) $13,911.69 Therefore, the present value of stream of cash flow that starts immediately and continues for 15 years is $13,911.69