Question

You invest $1,300 in an account that has an annual interest rate of 5%, compounded annually. How much money will be in the account after 10 years? Round your answer to the nearest whole number.

Answer 1

`\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1300\\ r=rate\to 5\%\to (5)/(100)\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases}`

`\bf A=1300\left(1+(0.05)/(1)\right)^(1\cdot 10)\implies A=1300(1.05)^(10)\implies \stackrel{\textit{rounded up}}{A=2118}`

Answer 2

A=Pe^rt

P= princible (1300)

e= (2.71828)- function on a graphing calculator

r = interest rate (.05 or 5%)

t = time (10 years)

A = 1300e^.05(10)

A = 1300e^.5

A = 2143.337652

A = 2143