## Amount of Annuity:

{eq}\\ {/eq}

The continuously compounded Annuity can be obtained using the formula {eq}\boxed{A=P\dfrac{e^{rn}-1}{e^r-1}} {/eq}, where P is the Payment made annually, r is the Rate of Interest per year and n is the time for which the payment is made.

An annuity is generally many numbers of installments that are made annually, monthly or maybe continuously.

## Answer and Explanation: 1

{eq}\\ {/eq}

Given : Payment paid per month= 220 $. So, the yearly payment will be {eq}220\times 12=2640 \$ {/eq}

{eq}\Rightarrow P=2640 \ $. {/eq} n= Number of years = 20 years. r= Rate of Interest = 8% per year = 0.08 per year. As we know that the formula for Annuity compounded continuously is given by:- {eq}A=P\dfrac{e^{rn}-1}{e^r-1} {/eq} Plugging the given values, we get :- {eq}\Rightarrow A=2640\dfrac{e^{20\times 0.08}-1}{e^{0.08}-1} {/eq} {eq}\Rightarrow A=2640\dfrac{e^{1.6}-1}{e^{0.08}-1} {/eq} {eq}\Rightarrow A=2640\dfrac{4.96-1}{1.08-1} {/eq} {eq}\Rightarrow A=2640\dfrac{3.96}{0.08} {/eq} {eq}\Rightarrow A=2640\times 49.5 {/eq} {eq}\Rightarrow \boxed{A=130680 \$.} {/eq}