In: Finance
Given
Purchase Price of a Car = $ 26000
Residual Value of Car at the end of 36 Months = 13000
Interest rate = 6% Compounded monthly
Interest rate per month = 6% /12 = 0.5% per Month
Computation of Present Value of Residual Value
We know that Present Value = Future Value / ( 1+i/12)^12n When interest is compounded monthly
Here I = Interest rate
n =No.of Years
Time period = 36 Months or 36/12 =3 Years
Present Value of Residual Value = 13000/ ( 1+0.06/12)^12*3
= 13000/ ( 1.005)^36
= 13000/1.196681
= 10863.38
Hence the Present Value of residual Value is 10863.38
Computation of Present value of lease payments
Purchase Price - Present Value of Residual Value = PV of Lease payments
26000-10863.38 = PV of Lease payments
15136.62 = PV of Lease payments
Computation of Lease payment amount
We know that Present Value of Ordinary Annuity = C [ {1- ( 1+i)^n }/i]
Here C = Cash Flow per period
I = Interest rate per period
n = No.of Payments
PV of Lease payments = C [ { 1-(1+0.005)^-36 }/0.005]
15136.62 = C [ { 1-(1.005)^-36 } /0.005]
15136.62= C [ { 1-0.835645}/0.005]
15136.62 = C [ 0.164355/0.005]
15136.62= C [ 32.87102]
15136.62/32.87102= C
C = 460.4853
Hence Lease payment amount should be 460.4853 per month
Lease payments during 36 months = 460.4853*36=16577.47
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