How to Calculate and Solve for Present Worth | Geometric Gradient | Economic Equivalence

The image above represents present worth. To calculate present worth, four essential parameters are needed and these parameters are First Payment (A₁), Interest Rate (i), Number of Year(s) (N) and Percentage change in payment (g).

The formula for calculating present worth:

P = A₁[1 – ((1 + g)^N)((1 + i)^-N)] / [i – g]

Where:

P = Present Worth or Amount
A₁ = First Payment
i = Interest Rate
g = Percentage change in payment
N = Number of Years

Let’s solve an example;
Find the present worth when the first payment is 10, the interest rate is 0.2, the percentage change in payment is 20 and the number of years is 5.

This implies that;

A₁ = First Payment = 10
i = Interest Rate = 0.2
g = Percentage change in payment = 0.1
N = Number of Years = 5

P = A₁[1 – ((1 + g)^N)((1 + i)^-N)] / [i – g]
P = 10[1 – ((1 + 0.1)⁵)((1 + i)^-(5))] / [0.2 – 0.1]
Then, P = 10[1 – ((1.1)⁵)((1.2)^-5)] / [0.1]
P = 10[1 – (1.61051)(0.401)] / [0.1]
P = 10[1 – 0.6472278485082308] / [0.1]
That is, P = 10[0.3527721514917692] / [0.1]
P = 10 x 3.527721514917692
P = 35.277215149176925

Therefore, the present worth is ₦35.28.

Read more: How to Calculate and Solve for Future Worth | Equal Payment Series | Economic Equivalence

How to Calculate Present Worth | Geometric Gradient With Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the present worth.

To get the answer and workings of the present worth using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

Web – https://www.nickzom.org/calculator-plus

To get access to the professional version via the web, you need to register and subscribe for NGN 1,500 per annum to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator

Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator
Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Economics under Engineering.

Now, Click on Economic Equivalence under Economics

Now, Click on Present Worth under Economic Equivalence

The screenshot below displays the page or activity to enter your values, to get the answer for the present worth according to the respective parameters which are the First Payment (A₁), Interest Rate (i), Number of Year(s) (N) and Percentage change in payment (g).

Now, enter the values appropriately and accordingly for the parameters as required by the First Payment (A₁) is 10, Interest Rate (i) is 0.2, Number of Year(s) (N) is 5 and Percentage change in payment (g) is 20.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the present worth and presents the formula, workings, and steps too.