On January 1, 2020, you are considering making an investment that will pay three annual payments of $10,000. The first payment is not expected until December 31, 2022. You are eager to earn 4%. What is the present value of the investment on January 1, 2020

$25,396.01

Explanation:

We first calculate the present value of the investment on December 31, 2022 using the present value (PV) of an  ordinary annuity as follows:

PV = P × [{1 - [1 ÷ (1+r)]^n} ÷ r] …………………………………. (1)

Where;

PV = Present value of the investment on December 31, 2022 = ?

P = yearly payments = $10,000

r = interest rate = 4% = 0.04

n = number of years = 43

Substitute the values into equation (1) to have:

PV = 10,000 × [{1 - [1 ÷ (1+0.4)]^3} ÷ 0.4] = 10,000 × 2.77509103322713 = $27,750.91

Since, the PV of the investment on December 31, 2022 is $27,750.91, we can now calculate its own PV in  January 1, 2020 which is 3 years as follows:

PV in January 2020 = $27,750.91 ÷ (1 + 0.4)^3 = $27,750.91 ÷ 1.092727 = $25,396.01  

It must have the same slope as the given line, so

m = -A/B = -1/-2 = 1/2

So far, we have

y = mx + b = x/2 + b

Use the given point to find b.

4 = -2/2 + b = -1 + b

b = 5

y = x/2 + 5

Multiply through by 2.

2y = x + 10

Standard form:

x - 2y = -10