Joan alexander wants to go on a long and luxurious vacation in three years. She could earn 8.20% compounded monthly in an account if she were to deposit the money today. She needs to have $10,000 in three years. How much will she have to deposit today?

Accepted Solution

Answer: $7825.86Step-by-step explanation:The formula to find the compound amount ( if compounded monthly) :-[tex]A=P(1+\dfrac{r}{12})^{12n}[/tex] , where n is number of years, r is  rate of interest and P is principal amount.Given : A=$10,000r=8.20%=0.082t= 3 yearsThen, the compounded amount will be :-[tex]10000=P(1+\dfrac{0.082}{12})^{12(3)}\\\\\Rightarrow\ 10000=P(1+0.006833)^{36}\\\\\Rightarrow\ 10000=P(1.27781474805)\\\\\Rightarrow\ P=\dfrac{10000}{1.27781474805}\\\\\Rightarrow\ P=7825.86052889\approx7825.86[/tex] [Rounded to nearest cent]Hence, she have to deposit $7825.86 today.