Question
Find the best balance
12,000 for 7 yrs at 5% simple interest or 12,000 for 7 yrs at 4:5% compound interest
12,000 for 7 yrs at 5% simple interest or 12,000 for 7 yrs at 4:5% compound interest
Answers
GPT-4o mini
To find the best balance between the two options, we need to calculate the total amount at the end of 7 years for both types of interest: simple and compound.
### Option 1: Simple Interest
The formula for calculating the total amount using simple interest is:
\[
A = P(1 + rt)
\]
Where:
- \(A\) = Total amount
- \(P\) = Principal amount (initial investment)
- \(r\) = Rate of interest (as a decimal)
- \(t\) = Time in years
For this option:
- \(P = 12,000\)
- \(r = 0.05\) (5%)
- \(t = 7\)
Now, substituting the values:
\[
A = 12000 \times (1 + 0.05 \times 7)
\]
\[
A = 12000 \times (1 + 0.35)
\]
\[
A = 12000 \times 1.35
\]
\[
A = 16200
\]
### Option 2: Compound Interest
The formula for calculating the total amount using compound interest is:
\[
A = P(1 + r)^t
\]
Where:
- \(r = 0.045\) (4.5%)
For this option:
- \(P = 12,000\)
- \(r = 0.045\)
- \(t = 7\)
Now, substituting the values:
\[
A = 12000 \times (1 + 0.045)^7
\]
Calculating \( (1 + 0.045)^7 \):
\[
A = 12000 \times (1.045)^7
\]
Calculating \( (1.045)^7 \):
\[
(1.045)^7 \approx 1.34885 \quad (\text{using a calculator for this})
\]
Now, substitute back:
\[
A \approx 12000 \times 1.34885 \approx 16186.20
\]
### Summary of the results:
- Total from Simple Interest: **16,200**
- Total from Compound Interest: **16,186.20**
### Conclusion:
The best balance after 7 years is provided by the Simple Interest option, totaling **16,200**, which is greater than the Compound Interest option totaling **16,186.20**.
### Option 1: Simple Interest
The formula for calculating the total amount using simple interest is:
\[
A = P(1 + rt)
\]
Where:
- \(A\) = Total amount
- \(P\) = Principal amount (initial investment)
- \(r\) = Rate of interest (as a decimal)
- \(t\) = Time in years
For this option:
- \(P = 12,000\)
- \(r = 0.05\) (5%)
- \(t = 7\)
Now, substituting the values:
\[
A = 12000 \times (1 + 0.05 \times 7)
\]
\[
A = 12000 \times (1 + 0.35)
\]
\[
A = 12000 \times 1.35
\]
\[
A = 16200
\]
### Option 2: Compound Interest
The formula for calculating the total amount using compound interest is:
\[
A = P(1 + r)^t
\]
Where:
- \(r = 0.045\) (4.5%)
For this option:
- \(P = 12,000\)
- \(r = 0.045\)
- \(t = 7\)
Now, substituting the values:
\[
A = 12000 \times (1 + 0.045)^7
\]
Calculating \( (1 + 0.045)^7 \):
\[
A = 12000 \times (1.045)^7
\]
Calculating \( (1.045)^7 \):
\[
(1.045)^7 \approx 1.34885 \quad (\text{using a calculator for this})
\]
Now, substitute back:
\[
A \approx 12000 \times 1.34885 \approx 16186.20
\]
### Summary of the results:
- Total from Simple Interest: **16,200**
- Total from Compound Interest: **16,186.20**
### Conclusion:
The best balance after 7 years is provided by the Simple Interest option, totaling **16,200**, which is greater than the Compound Interest option totaling **16,186.20**.