A company is planning to purchase a plot of land for $200,000 to build a factory. There are two options offered by a lending institution.
- 20-year loan at 3.25% APR compound monthly
- 30-year loan at 4.75% APR compound monthly
Where you need to:
- Calculate the monthly payment for both options.
- Calculate the finance charge for both options.
- Determine which option is better for the company & explain why
Answer
1. To calculate the monthly payment for a loan, you can use the following formula: P = L[c(1 + c)^n]/[(1 + c)^n – 1], where P is the monthly payment, L is the loan amount, c is the monthly interest rate (in decimal form), and n is the number of payments. For the 20-year loan at 3.25% APR, the monthly interest rate is 3.25%/12 = 0.00270833, and the number of payments is 2012 = 240. Plugging these values into the formula, we get: P = 200,000[0.00270833(1 + 0.00270833)^240]/[(1 + 0.00270833)^240 – 1] = $1,204.08. For the 30-year loan at 4.75% APR, the monthly interest rate is 4.75%/12 = 0.00395833, and the number of payments is 3012 = 360. Plugging these values into the formula, we get: P = 200,000[0.00395833(1 + 0.00395833)^360]/[(1 + 0.00395833)^360 – 1] = $1,045.63
2. To calculate the finance charge for a loan, you can use the following formula: Finance Charge = (Monthly Payment x Number of Payments) – Principal. For the 20-year loan at 3.25% APR, the finance charge is (1204.08 x 240) – 200,000 = $111,768. For the 30-year loan at 4.75% APR, the finance charge is (1045.63 x 360) – 200,000 = $214,636.
3. The 20-year loan at 3.25% APR is the better option for the company. The company will pay a lower monthly payment and a lower finance charge over the life of the loan. The company will pay off the loan faster and will pay less in interest charges.
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