Question

How much would Zion earn on a deposit of $10,000 one year at 5.12% compounded daily?
$525.30
$10,512.00
$10,523.30
$512.00

Answer 1

To calculate the amount Zion would earn on a deposit of $10,000 at an interest rate of 5.12% compounded daily for one year, we can use the formula for compound interest:

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

where:
- \( A \) = the amount of money accumulated after n years, including interest.
- \( P \) = the principal amount (the initial amount of money).
- \( r \) = the annual interest rate (decimal).
- \( n \) = the number of times that interest is compounded per year.
- \( t \) = the number of years the money is invested or borrowed.

Given:
- \( P = 10,000 \)
- \( r = 5.12\% = 0.0512 \)
- \( n = 365 \) (compounded daily)
- \( t = 1 \)

Plugging in the values:

\[
A = 10,000 \left(1 + \frac{0.0512}{365}\right)^{365 \cdot 1}
\]

Calculating:

1. Calculate \( \frac{r}{n} \):

\[
\frac{0.0512}{365} \approx 0.0001408219
\]

2. Calculate \( 1 + \frac{r}{n} \):

\[
1 + 0.0001408219 \approx 1.0001408219
\]

3. Calculate \( nt \):

\[
365 \cdot 1 = 365
\]

4. Now calculate:

\[
A = 10,000 \left(1.0001408219\right)^{365}
\]

Using a calculator to find \( (1.0001408219)^{365} \):

\[
(1.0001408219)^{365} \approx 1.051712
\]

5. Finally calculate \( A \):

\[
A \approx 10,000 \times 1.051712 \approx 10,517.12
\]

Now to find the earned interest:

\[
\text{Interest Earned} = A - P = 10,517.12 - 10,000 \approx 517.12
\]

Since the earnings closely match the options provided, we can round this to an appropriate amount.

The closest answer from the options given is **$512.00**.