Questions: Nelda deposited 500 in a bank that is paying 2% interest daily. Identify the function P that represents the amount of money she will have after t years. A. P=500 e^0.02 t B. P=500(1.02)^t C. P=500 e^1.02 t D. P=500(1+0.02/12)^12 t E. P=500(1+0.02/365)^365 t

Solution Steps

The formula for compound interest is given by

\[ P = P_0 \left(1 + \frac{r}{n}\right)^{nt} \]

where:

• \( P_0 = 500 \) (initial deposit),
• \( r = 0.02 \) (annual interest rate),
• \( n = 365 \) (number of compounding periods per year),
• \( t \) (time in years).

Substituting the known values into the formula, we have:

\[ P = 500 \left(1 + \frac{0.02}{365}\right)^{365t} \]

To find the amount after \( t = 1 \) year, we substitute \( t = 1 \) into the equation:

\[ P = 500 \left(1 + \frac{0.02}{365}\right)^{365 \cdot 1} \]

Calculating this gives:

\[ P \approx 510.1003905164615 \]

Thus, the amount after 1 year is approximately \( 510.10 \).

Final Answer