Math, asked by moonexol1407, 21 days ago

A contract requires lease payments of $800 at the beginning of every month for 5 years.
a. What is the present value of the contract if the lease rate is 4.75% compounded annually?
b. What is the present value of the contract if the lease rate is 4.75% compounded monthly?

Answers

Answered by santoshyograj
0

Answer:

dont know answer get soon

Answered by amitnrw
0

Given : A contract requires lease payments of $800 at the beginning of every month for 5 years.

To Find : the present value of the contract if the lease rate is 4.75% compounded monthly?

Solution:

Let Say present Value = N $

Value after 1st Deposit as its in beginning = N - 800 $

Now EMI of 800 $ for 59 times    as there are 60 months in 5 years and one payment is already done

and rate = 4.75 % per annum = 4.75/12    % per month

Apply EMI formula

EMI Formula =  [P x (R/100) x (1+(R/100))ⁿ]/[(1+(R/100))ⁿ-1]

P = N - 800 $

R = 4.75/12    % per month

n = 59 months

EMI = 800

=> 800  =    (N - 800) * (4.75/1200) *  ( 1 + 4.75/1200)⁵⁹/(( 1 + 4.75/1200)⁵⁹- 1)

=>  800  =    (N - 800) * (4.75/1200) *  4.81

=> 42,019.77 = N -800

=> N = 42,819.77

=> N  ≈ 42820  $

Present value is  42820  $

Lease rate is 4.75% compounded annually

paid before 1st year = 9600 $

P = N - 9600   $

EAI = 9600 $

9600  = ( N - 9600) * (4.75/100) *  ( 1 + 4.75/100)⁴/(( 1 + 4.75/100)⁴- 1)

=> 9600 =  ( N - 9600) * (4.75/100) *  5.90265

=> 34,239.74 =  N - 9600

=> N = 43,839.74  

=> N ≈  43,840

Present value is  43,840 $

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