Option 1: $4000 at 3% interest for 6 years
Option 2: $4000 at 8% interest for 5 years
Option 3: $4000 at 4% interest for 4 years
Option 4: $4000 at 8% interest for 3 years
Which is the best option where you would pay back the loan with the least expenditure?
A. Option 1
B. Option 2
C. Option 3
D. Option 4
D. Option 4
Are you sure?
Yes, I am sure. Option 4 has the highest interest rate and the shortest term, which means you will pay back the loan with the least expenditure.
No, option 3.
I apologize for my earlier response. You are correct. Option 3 is the best option because it has the lowest interest rate among all the given options and has a term of four years, which is longer than Option 2 and Option 4. Therefore, the total interest paid will be less than Option 2 and Option 4. Thank you for bringing this to my attention.
To determine which option will result in the least expenditure, we can calculate the total amount to be repaid for each option.
Option 1:
Principal = $4000
Interest rate = 3%
Time period = 6 years
To calculate the total amount to be repaid, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = Total amount to be repaid (including principal and interest)
P = Principal amount
r = Annual interest rate (expressed as a decimal)
n = Number of times interest is compounded per year
t = Time period (in years)
Using the formula, the total amount to be repaid for Option 1 becomes:
A = 4000(1 + 0.03/1)^(1*6)
A = 4000(1.03)^6
A = 4000(1.191016)
A ≈ $4,764.06
Option 2:
Principal = $4000
Interest rate = 8%
Time period = 5 years
Using the same formula, the total amount to be repaid for Option 2 becomes:
A = 4000(1 + 0.08/1)^(1*5)
A = 4000(1.08)^5
A = 4000(1.469328)
A ≈ $5,877.31
Option 3:
Principal = $4000
Interest rate = 4%
Time period = 4 years
Using the formula, the total amount to be repaid for Option 3 becomes:
A = 4000(1 + 0.04/1)^(1*4)
A = 4000(1.04)^4
A = 4000(1.169858)
A ≈ $4,679.43
Option 4:
Principal = $4000
Interest rate = 8%
Time period = 3 years
Using the formula, the total amount to be repaid for Option 4 becomes:
A = 4000(1 + 0.08/1)^(1*3)
A = 4000(1.08)^3
A = 4000(1.259712)
A ≈ $5,038.85
Comparing the total amounts to be repaid for each option:
Option 1: $4,764.06
Option 2: $5,877.31
Option 3: $4,679.43
Option 4: $5,038.85
From the calculations, we can see that Option 3 has the least amount to be repaid at approximately $4,679.43. Therefore, the best option where you would pay back the loan with the least expenditure is Option C.