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
Answer:
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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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