Question

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?

Answer 1

$3649.11

Step-by-step explanation:

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

`A=P(1+(r)/(n))^(nt)`

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;

`\begin{gathered} 5000=P(1+(0.105)/(365))^(365*3) \\ 5000=P(1.370) \\ P=(5000)/(1.37) \\ P=3649.11 \end{gathered}`