Question

A contract requires lease payments of $900 at the beginning of every month for 3 years.

a. What is the present value of the contract if the lease rate is 5.50% compounded annually?

b. What is the present value of the contract if the lease rate is 5.50% compounded monthly?

Answer 1

- Lease Payment at the beginning of each month for 3 years = $900

a) lease rate = 5.50%compounded annually

Calculating Lease Rate compounded monthly using the Effective Annual rate(EAR) formula:-

where, r = Lease rate compounded monthly

m = no of times compunding in a year = 12

EAR = 5.50%

1.004472 = (1+ r/12)

r = 5.3664%

So, Lease Rate compounded monthly is 5.3664%

Calculating the Present value of the contract:-

Where, C= Periodic Payments = $900

r = Periodic Interest rate = 5.3664%/12 = 0.4472%

n= no of periods = 3 years*12 = 36

Present Value = $29,998.49

b) lease rate = 5.50% compounded monthly

Calculating the Present value of the contract:-

Where, C= Periodic Payments = $900

r = Periodic Interest rate = 5.50%/12 = 0.458333%

n= no of periods = 3 years*12 = 36

Present Value = $29,941.98

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