For the classic exam-style problem “what is the present worth of two 100 payments at the end of the third year and fourth year at 8% interest,” the present worth is about 153 (in the same currency as the payments).

Quick Scoop

You’re dealing with present worth (present value): how much two future 100 payments are worth today , given an 8% annual interest rate.

The general formula for the present worth of each payment is:

  • PV=100(1+0.08)nPV=\dfrac{100}{(1+0.08)^n}PV=(1+0.08)n100​ where nnn is the number of years until that payment.

So you do:

  • Third-year payment: discount back 3 years
  • Fourth-year payment: discount back 4 years
  • Then add those two present values together.

Worked example from standard solutions:

  • Present value of 100 at end of year 3 ≈ 79.41
  • Present value of 100 at end of year 4 ≈ 73.49
  • Total present worth ≈ 79.41 + 73.49 ≈ 152.90, which is usually rounded and reported as 153.

Tiny “story” version

Imagine you could either:

  1. Get about 153 now, or
  2. Wait and get 100 at the end of year 3 and 100 at the end of year 4, while money is “growing” at 8% per year.

Those two options are financially equivalent under an 8% rate—so the “present worth” of those two future 100 payments is roughly 153.

TL;DR: With two 100 payments at the end of years 3 and 4 and an 8% interest rate, the present worth is about 153.

Information gathered from public forums or data available on the internet and portrayed here.