Sauerfood company has decided to buy a new computer system with an expected life of 3 yrs. the cost is 150,000.the comapny can borrow $150,000 for 3yrs at 10% annual interest or for one yr at 8% annual interest. How much wld sauer save in interest over the 3 yr life of the computer system if the one year loan is utilized and the loan is rolled over each yr at the same 8% rate?compare this to the 10% 3 yr loan. what if interest rates on the 8% loan go up by 13% in year 2 and 18% in yr 3? what would be the total interest cost compared to the 10% ,3 year loan?
To determine how much Sauerfood company would save in interest over the 3-year life of the computer system, we need to calculate the interest costs for both loan options and compare them.
Option 1: 3-year loan at 10% annual interest
Using the formula to calculate compound interest, we can find the interest cost for this loan:
Interest = Principal * (1 + Rate)^Time - Principal
Principal = $150,000
Rate = 10% = 0.10
Time = 3 years
Interest = $150,000 * (1 + 0.10)^3 - $150,000
Interest = $150,000 * (1.10^3) - $150,000
Interest = $150,000 * 1.331 - $150,000
Interest = $199,650 - $150,000
Interest = $49,650
Therefore, the interest cost for the 3-year loan at 10% annual interest would be $49,650.
Option 2: 1-year loan at 8% annual interest rolled over each year
Since the loan is rolled over each year, we'll calculate the interest cost annually and then sum them up.
Year 1:
Interest = Principal * Rate = $150,000 * 0.08 = $12,000
Year 2:
Interest = Principal * (1 + Rate)^Time - Principal = $150,000 * (1 + 0.08)^1 - $150,000 = $16,200
Year 3:
Interest = Principal * (1 + Rate)^Time - Principal = $150,000 * (1 + 0.08)^2 - $150,000 = $17,496
Total interest cost for the 1-year loan rolled over each year = $12,000 + $16,200 + $17,496 = $45,696
The savings in interest over the 3-year life of the computer system using the 1-year loan rolled over each year compared to the 3-year loan at 10% annual interest would be $49,650 - $45,696 = $3,954.
Now, let's consider what happens if the interest rates on the 8% loan increase by 13% in year 2 and 18% in year 3.
Year 1 remains the same: $12,000
Year 2:
Interest = Principal * (1 + Rate)^Time - Principal = $150,000 * (1 + 0.08)^1 - $150,000 = $16,200
Year 3:
New Interest Rate = 8% + 13% = 21%
Interest = Principal * (1 + Rate)^Time - Principal = $150,000 * (1 + 0.21)^1 - $150,000 = $31,500
Total interest cost for the 1-year loan with increased rates = $12,000 + $16,200 + $31,500 = $59,700
The total interest cost for the 3-year loan at 10% annual interest remains $49,650.
Therefore, the total interest cost for the 8% loan with increased rates compared to the 3-year loan at 10% annual interest would be $59,700 - $49,650 = $10,050.