Respuesta :
Answer:
Present value of the loan = $15,877
Explanation:
One thing that one must master with this type of question is how to choose between a present value factor and a present value annuity factor. If the solution to a question calls for discounting a single payment or a set of payments with different amounts, then one should use present value factors. If the question calls for discounting an annuity, which is a series of equal payments at equal intervals, then one should use a present value annuity factor.
In this question, the company must repay a single payment of $20,000 in 3 years. to find the present value we discount this payment that is to made at the end of year 3 by multiplying with the present value factor for 3 years at 8% is 0.7938 i.e
[tex]PV=$20,000*0.7938 = $15,877[/tex]
Alternatively one can use a tabular format to visualise what is happening as follows:
Year Cash-flow PV factor at 8% Present value
1 - 0.9259 $0.00
2 - 0.8573 $0.00
3 $20,000 0.7938 $15,876.64
Present Value $15,876.64
Based on the explanation and calculation below, the present value of the loan is $15,876.
What is the present value (PV)?
Given a certain interest rate, present value can be described as the current value of a future sum of money or stream of cash flows.
It should be noted from the definition that to calculate the PV of a future sum of money, the present value factor is used.
However, to calculate the PV of a future stream of cash flows, the present value of an annuity factor.
Since the single payment of $20,000 cash in 3 years is a future sum of money, the present value factor is therefore used to calculate its present value as follows:
Present value of the loan = $20,000 * Present value factor = $20,000 * 0.7938 = $15,876
Learn more about present value here: https://brainly.com/question/17322936.
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