What is the initial amount, rounded to the nearest cent, that you would need to invest into an account earning 10.5% interest compounded daily, to have $5000 in a 3 year time span?

Respuesta :

Answer:

$3649.11

Explanation:

The below formula for compound interest will be used to solve the given problem;

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where A = the final amount = $5000

P = the initial amount

r = annual interest rate( in decimal form) = 10.5% = 10.5/100 = 0.105

n = number of times compounded per year = 365

t = time in years = 3

Let's go ahead and substitute the given values into the formula and solve for P as shown below;

[tex]\begin{gathered} 5000=P(1+\frac{0.105}{365})^{365\times3} \\ 5000=P(1.370) \\ P=\frac{5000}{1.37} \\ P=3649.11 \end{gathered}[/tex]