If an initial amount Ao of money is invested at an interest rate r compounded n times a year, the value of the investment after t years is 𝐴 = 𝐴o 1 + 𝑟n nt. If the interest is compounded continuously, (that is as n→∞), show that the amount after t years is A = Aoert.

If an initial amount Ao of money is invested
at an interest rate r compounded n
times a year, the value of the investment
after t years is $𝐴 = 𝐴_{o} {(1 + \frac{𝑟}{n})}^{n t}$ . If the
interest is compounded continuously,
(that is as n $\to \infty$ ), show that the amount
after t years is A = $A_{o} e^{r t} .$

Matching exercise

Match the items on the right to the items on the left.

Step - 1

Step - 2

Step - 3

Step - 4