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Answer: Effective Annual Interest Rate
- Calculate the total cost of the first option, which involves paying $100 today and $1,300 in 8 months. To do this, we need to find the present value of the second payment using the monthly interest rate. Assuming a monthly interest rate of r, we have:
PV = 1300/(1+r/12)^8
The total cost is therefo
TC1 = 100 + PV
- Calculate the total cost of the second option, which involves paying $1,200 today. This is simply:
TC2 = 1200
- Set TC1 equal to TC2 and solve for r. We have:
100 + PV = 1200
PV = 1100
1100 = 1300/(1+r/12)^8
(1+r/12)^8 = 1.1818
1+r/12 = 1.018
r = 0.216 or 21.6%
- Convert the monthly interest rate to an effective annual interest rate. We have:
(1+r/12)^12 - 1 = 0.265 or 26.5%
Therefore, the effective annual interest rate being implicitly charged is approximately 26.5%. This means that if you choose the first option and pay $100 today and $1,300 in 8 months, you are effectively paying an interest rate of 26.5% per year, assuming monthly compounding.
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