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Abigail has just signed a 5-year lease for her new business. The full annual lease amount is due at the beginning of every year and such cash flows have been agreed to be 20,156 dollars now and the subsequent payments to increase by 5% per year until maturity. Given that the prevailing average market interest rate is 8% per year compounded monthly, compute the present value of this financial asset. (note: round your answer to the nearest cent and do not include spaces, currency signs, or commas)

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Parrain

Answer: $93,088

Explanation:

Rate is compounded monthly which makes it:

= 8% / 12

= 0.6667%

= 0.006667

The payment of $20,156 is to increase yearly at a rate of 5%. Payments are at the beginning of the period so the first payment does not have to be discounted.

[tex]= 20,156 + \frac{20,156 * 1.04}{(1 + 0.006667)^{12} } + \frac{20,156 * 1.04^{2} }{(1 + 0.006667)^{24} } + \frac{20,156 * 1.04^{3} }{(1 + 0.006667)^{36} } + \frac{20,156 * 1.04^{4} }{(1 + 0.006667)^{48} }\\\\= 20,156 + 19,355.65 + 18,587.08 + 17,849.02 + 17,140.27\\\\= 93,088.02[/tex]

= $93,088

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