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Short Company purchased land by paying $10,000 cash on the purchase date and agreeing to pay $10,000 for each of the next ten years beginning one-year from the purchase date. Short's incremental borrowing rate is 10%. The land reported on the balance sheet is closest to:
(A) $100,000
(B) $38,550
(C) $61,446
(D) $71,446

Respuesta :

TomShelby

Answer:

(D) $71,446

Explanation:

we will calcualte the present value for an 11 payments  annuity-due (there is eleven payment of 10,000 if we count the one at purchase date) which couta is 10,000 discounted at 10%

[tex]C \times \frac{1-(1+r)^{-time} }{rate} (1 +r ) = PV\\[/tex]

C 10,000

time 11

rate 0.1

[tex]10000 \times \frac{1-(1+0.1)^{-11} }{0.1} (1 + 0.10) = PV\\[/tex]

PV $71,445.6711

rounding to the nearest dollars: 71,446