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  

month 1 start amount =$3287.90 interest=(3287.90x0.0145/12)3.97 total to pay=$3291.81 paid =$1200 balance =$2,091.87

month 2 starting amount= $2,091.87 interest =$25.28 total to pay =$2117.15 paid =$1200 balance $917.15

month 3 starting amount =$917.15 interest =$11.08 total to pay =$928.23 paid =$928.23 balance =$0 total to pay 1200+1200+928.23 = $3328.23 it will take 3 months to pay a total of $3328.23

answer; commerce clearing house;