MHB Calculate Present Value of 10-Year Lease w/ OCC & Variable Rental

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The discussion revolves around calculating the present value of a 10-year lease with annual payments that increase by 2% each year, starting at £20, with an opportunity cost of capital (OCC) of 10%. The original poster initially calculated a present value of -£23.88, while the book states it should be £132.51. Participants suggest that the error likely stems from incorrect data entry into the calculator. A corrected formula is provided, emphasizing the importance of accurate input for the calculation. The conversation concludes with the poster confirming the use of the correct figures resolved the issue.
logicandtruth
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Hi all

Trying to improve my level of maths and would like some help with the below question please.

A 10-year lease with annual rental payments to be made at the end of each year, with the rent increasing by 2% each year. If the first year rent is £20 and the OCC is 10% per year, what is the Present value of the lease?

The formula for present value of a level annuities is below (for a growing interest rate)

View attachment 8227

According to my book the answer should be £132.51, but I get -23.88.

View attachment 8228

Could anyone tell me where I am misinterpreting the formula?
 

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Book is correct. Are you using a calculator?
You're probably entering the data wrongly...we can't tell...
Try it this way:
u = (1.02/1.10)^10
v = .10 - .02

PV = 20*(1 - u) / v
 
Yes it works I must have been using the incorrect figure with my calculator.

Many thanks
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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