Question

Joshua deposits $650
into a savings account that pays 1.53%
simple annual interest.
What is Joshuas account balance after
21 months?

Answer 1

To calculate the balance in Joshua's account after 21 months with simple interest, we can use the formula for simple interest:

\[
A = P + I
\]

where:
- \( A \) is the total amount in the account after the interest is added,
- \( P \) is the principal amount (initial deposit),
- \( I \) is the interest earned.

The interest \( I \) can be calculated using the formula:

\[
I = P \times r \times t
\]

where:
- \( r \) is the annual interest rate (in decimal form),
- \( t \) is the time the money is invested or borrowed for, in years.

1. **Convert the annual interest rate from percentage to decimal:**
- \( r = 1.53\% = \frac{1.53}{100} = 0.0153 \)

2. **Convert the time from months to years:**
- \( t = \frac{21 \text{ months}}{12} = 1.75 \text{ years} \)

3. **Calculate the interest \( I \):**
\[
I = P \times r \times t = 650 \times 0.0153 \times 1.75
\]

\[
I = 650 \times 0.0153 \times 1.75 = 650 \times 0.026775 = 17.40375
\]

4. **Calculate the total amount \( A \) in the account:**
\[
A = P + I = 650 + 17.40375 = 667.40375
\]

Therefore, the account balance after 21 months is approximately **$667.40**.