Question

$500 invested at 6.25% per year compounded daily for 3 years= Round to the nearest cent

Answer 1

This is a compound interest problem:

Step 1: List out the given parameters

`\begin{gathered} \text{Amount (A) = unknown} \\ Principal(P)=500\text{ dollars} \\ \text{Rate (r) = 6.25 percent} \\ Time(t)=3\text{ years} \\ \text{Number of times compounded (n) = 365 days} \end{gathered}`

Step 2: Write out the compound interest formula:

`A=P\lbrack1+(r)/(n100)\rbrack^(nt)`

Step 3: Substitute the given parameters into the compound interest formula:

`\begin{gathered} A=P\lbrack1+(r)/(n100)\rbrack^(nt) \\ A=500\lbrack1+(6.25)/(365*100)\rbrack^(365*3) \end{gathered}`

Simplifying further:

`\begin{gathered} A=500\lbrack1+(6.25)/(36500)\rbrack^(1095) \\ A=500\lbrack1+0.00017123\rbrack^(1095) \\ A=500\lbrack1.00017123\rbrack^(1095) \\ A=500*1.2062071 \\ A=603.10355\text{ dollars} \\ A=603.10\text{ dollars (to the nearest cent)} \end{gathered}`

The answer is $603.10.