Question

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?

Answer 1

Answer: $7825.86

Step-by-step explanation:

The formula to find the compound amount ( if compounded monthly) :-

$A=P(1+\dfrac{r}{12})^{12n}$ , where n is number of years, r is  rate of interest and P is principal amount.

Given : A=$10,000

r=8.20%=0.082

t= 3 years

Then, the compounded amount will be :-

$10000=P(1+\dfrac{0.082}{12})^{12(3)}\\\\\Rightarrow\ 10000=P(1+0.006833)^{36}\\\\\Rightarrow\ 10000=P(1.27781474805)\\\\\Rightarrow\ P=\dfrac{10000}{1.27781474805}\\\\\Rightarrow\ P=7825.86052889\approx7825.86$ [Rounded to nearest cent]

Hence, she have to deposit $7825.86 today.