Final answer:
The total amounts at the beginning of the lease for each situation are $553,675.75, $534,442.01, $560,482.58, and $530,815.40.
Step-by-step explanation:
To determine the amounts at the beginning of the lease, we need to calculate the present value of the lease payments and the present value of the residual value. Here are the steps for each situation:
- Situation 1: Lease term is 7 years and interest rate is 9%. The present value of the lease payments is $553,675.75 ($100,000 * 5.5367575) and the present value of the residual value is $0. The total amount at the beginning of the lease is $553,675.75.
- Situation 2: Lease term is 7 years and interest rate is 11%. The present value of the lease payments is $499,987.56 ($100,000 * 4.9998756) and the present value of the residual value is $34,454.45 ($50,000 * 0.689089). The total amount at the beginning of the lease is $534,442.01.
- Situation 3: Lease term is 8 years and interest rate is 10%. The present value of the lease payments is $553,680.06 ($100,000 * 5.5368006) and the present value of the residual value is $6,802.52 ($8,000 * 0.8503165). The total amount at the beginning of the lease is $560,482.58.
- Situation 4: Lease term is 8 years and interest rate is 12%. The present value of the lease payments is $494,362.75 ($100,000 * 4.9436275) and the present value of the residual value is $36,452.65 ($50,000 * 0.729053). The total amount at the beginning of the lease is $530,815.40.