a) The value of the original lease contract is approximately 39,148.19.
b) Amount needed to bring the lease payments up to date is 6,102.32.
c) The amount required to pay off the lease after nine months is approximately 37,206.64.
d) Total interest is approximately 3,865.91.
e) Approximately2,045.87 of the total interest is due to deferring the first eight payments.
a) To calculate the value of the original lease contract, we can use the formula for the present value of an annuity:
PV = PMT * ((1 - (1 + r)^(-n)) / r)
Where:
PMT = lease payments = 762.79
r = monthly interest rate = 15% / 12 = 0.15 / 12 = 0.0125
n = total number of payments = 6 years * 12 months/year = 72
PV = 762.79 * ((1 - (1 + 0.0125)^(-72)) / 0.0125)
PV ≈39,148.19
So, the value of the original lease contract is approximately 39,148.19.
b) If the first eight payments were deferred, the amount needed after nine months to bring the lease payments up to date would be the sum of the missed payments:
Amount needed = 762.79 * 8
Amount needed =6,102.32
c) To calculate the amount required to pay off the lease after nine months, we can use the formula for the present value of an annuity again, but with fewer payments remaining:
PV = PMT * ((1 - (1 + r)^(-n)) / r)
Where:
PMT = lease payments = 762.79
r = monthly interest rate = 15% / 12 = 0.15 / 12 = 0.0125
n = remaining number of payments = 6 years * 12 months/year - 9 months = 69
PV = 762.79 * ((1 - (1 + 0.0125)^(-69)) / 0.0125)
PV ≈37,206.64
So, the amount required to pay off the lease after nine months is approximately 37,206.64.
d) The total interest paid if the lease were paid off after nine months can be calculated by subtracting the original value of the lease contract from the total amount paid:
Total interest = Total amount paid - PV
Total interest = (762.79 * 9) - 39,148.19
Total interest ≈3,865.91
e) To find out how much of the total interest is due to deferring the first eight payments, we can calculate the interest on the missed payments and subtract it from the total interest:
Interest on missed payments = Amount needed - PV
Interest on missed payments = 6,102.32 - 39,148.19
Interest on missed payments ≈ 2,045.87
So, approximately2,045.87 of the total interest is due to deferring the first eight payments.