can some one help me in this question 1.37 pg-13 ques bank. why have they taken 200-10t while doing integration. thanks
This is because 200-10t is the continuous rate of payment which needs to be summed up by use of integrals.
You're actually quite close to getting the right answer. Basically, the question says that the annuity is initially paid at a rate of $200 pa (continuously) but decreases linearly to $100 pa after 10 years. This means that the rate of payment is 200 - 10t where t is the time elapsed in years. It appears that your calculation does not factor in the decreasing component. Your calculation would otherwise be correct if the annuity was simply paid at a rate of $200 pa without any adjustment over time. Hope that helps!