Respuesta :
Given:
a.) A company will need 1.8 million 5 years from now to replace some equipment.
b.) The account pays 5.25 percent interest, compounded annually.
We will be applying the Compounded Interest Formula:
[tex]\text{ A = P\lparen1 + }\frac{r}{n})^{nt}[/tex]Where,
A=final amount
P=initial principal balance/money to initially deposit
r=interest rate (decimal)
n=number of times interest applied per time period
t=number of time periods elapsed (in years)
In this scenario, we are asked what is the amount of principal balance/initial deposit to make to get 1.8 million in 5 years.
Annually = n = 1
We get,
[tex]\text{ 1,800,000 = P\lparen1 + }\frac{\frac{5.25}{100}}{1})^{(1)(5)}[/tex][tex]1,800,000\text{ = P \lparen1 + 0.0525\rparen}^5\text{ = P \lparen1.0525\rparen}^5[/tex][tex]\text{ P = }\frac{1,800,000}{(1.0525)^5}[/tex][tex]\text{ P = 1,393,676.5175887556 }\approx\text{ 1,393,676.52}[/tex]Therefore, the answer is 1,393,676.52
