Let's work through each of the missing values step-by-step using the simple interest formula:

$\text{Interest (I)} = \text{Principal (P)} \times \text{Rate (R)} \times \text{Time (T)}$

Where:

• $P$ is the principal amount,
• $R$ is the rate (expressed as a decimal),
• $T$ is the time in years.

Let’s solve for each missing item:

Row 1

• Principal: 8500
• Time: 4 years
• Final Amount (A): 9690

From the final amount and principal, we can find the interest: $I = A - P = 9690 - 8500 = 1190$

Using this, we can now solve for the rate: $R = \frac{I}{P \times T} = \frac{1190}{8500 \times 4} = 0.035 \text{ or } 3.5\%$

So, Rate = 3.5% and Interest = 1190.

Row 2

• Principal: Unknown
• Rate: 6%
• Time: 7 years and 3 months (7.25 years in decimal form)
• Interest: 900

Rearrange the formula to solve for $P$: $P = \frac{I}{R \times T} = \frac{900}{0.06 \times 7.25} \approx 2068.97$

So, Principal = 2068.97.

Now, the final amount: $A = P + I = 2068.97 + 900 = 2968.97$

So, Final Amount = 2968.97.

Row 3

• Principal: 17700
• Rate: 4.5%
• Time: From 08/05/22 to 03/21/23

Calculating the exact time in days between 08/05/22 and 03/21/23:

1. August 5, 2022, to March 21, 2023, is 228 days.

Convert days to years: $T = \frac{228}{365} \approx 0.6247 \text{ years}$

Now, calculate the interest: $I = P \times R \times T = 17700 \times 0.045 \times 0.6247 \approx 497.33$

Then, the final amount: $A = P + I = 17700 + 497.33 = 18197.33$

So, Interest = 497.33 and Final Amount = 18197.33.

If you’d like further details or have any questions on each calculation, please let me know!

Questions for Further Exploration

1. How is simple interest calculated differently from compound interest?
2. What is the impact of rounding on the final answer in financial calculations?
3. How would the answers change if the interest were compounded annually?
4. Can you calculate the interest for a leap year (366 days)?
5. What is the significance of converting time to years when calculating simple interest?

Tip

Always double-check the time conversions, especially when dealing with months or days, to ensure accuracy in financial calculations.