If an initial amount `A_(0)` of money is invested at an interest rate r compounded n times a year, the value of the investment after t years is `A=A_(0)(1+1/n)^(nt)`. If the interest is compounded continuously, (that is as `ntooo`), show that the amount after t years is `A=A_(0)e^(rt)`.

What constant interest rate is required if an initial deposit placed into an account accrues interest compounded continuously is to double its value in six years? (ln|x|=0. 6930)

₹1000 is invested at 10 percent simple interest. Check at the end of every year if the total interest amount is in A.P. If this is an A.P. the find interest amount after 20 years. For this complete the following activity.

Express each of the following physical statements in the form of differential equation. (iv) A saving amount pays 8% interest per year, compounded continuously. In addition, the income from another investment is credited to the amount continuoulsy at the rate of Rs. 400 per year.

In a bank, principal increases continuously at the rate of r% per year.Find the value of r if Rs 100 double itself in 10 years (log_(e)2 = 0.6931) .

A share is sold for the market value of Rs 1000 Brokerage is paid at the rate of 0.1% .What is the amount received after the sale ?

Consider a tank which initially holds V_(0) liter of brine that contains a lb of salt. Another brine solution, containing b lb of salt per liter is poured into the tank at the rate of eL//"min" . The problem is to find the amount of salt in the tank at any time t. Let Q denote the amount of salt in the tank at any time. The time rate of change of Q, (dQ)/(dt) , equals the rate at which salt enters the tank at the rate at which salt leaves the tank. Salt enters the tank at the rate of be lb/min. To determine the rate at which salt leaves the tank, we first calculate the volume of brine in the tank at any time t, which is the initial volume V_(0) plus the volume of brine added et minus the volume of brine removed ft. Thus, the volume of brine at any time is V_(0)+et-ft The concentration of salt in the tank at any time is Q//(V_(0)+et-ft) , from which it follows that salt leaves the tank at the rate of f(Q/(V_(0)+et-ft)) lb/min. Thus, (dQ)/(dt)=be-f(Q/(V_(0)+et-ft))Q=be A tank initially holds 100 L of a brine solution containing 20 lb of salt. At t=0, fresh water is poured into the tank at the rate of 5 L/min, while the well-stirred mixture leaves the tank at the same rate. Then the amount of salt in the tank after 20 min.

What will Rs. 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?