Question

Which equation represents the situation:

Jasper has $154.65 to put into a savings account. The savings account has a 2.3% interest rate compounded weekly.

A = 154.65 (1 +.023)^t

154.65 (1+ .023/7)^7t

A=154.65 ( 1+.023/52)^52t

A=154.65 (1+.23/52)

Answer 1

To represent the situation where Jasper has $154.65 to put into a savings account with a 2.3% interest rate compounded weekly, we need to use the compound interest formula:

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

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

In this case:
- \( P = 154.65 \)
- \( r = 0.023 \) (since 2.3% as a decimal is 0.023)
- Since the interest is compounded weekly, \( n = 52 \) (there are 52 weeks in a year).

Now, substituting these values into the compound interest formula, we have:

\[ A = 154.65 \left(1 + \frac{0.023}{52}\right)^{52t} \]

Among the provided options, this matches:

**A = 154.65 ( 1 + .023/52)^52t**

Thus, this is the correct equation representing the situation.