Back Solve for the Starting Loan Amount

[baileyisnotreal]

Trying to solve for the starting Loan Value knowing the annual yield and the required interest rate with a formula. Or how much I would pay for a Bond knowing the annual payments and my required interest rate if the bond payments were the same every year. Same thing:

• Known Variables:
  • (A) Uneven (but growing) cash flows / yield that 100% goes towards the Lender
  • (B) Dates of cash flows / yield
  • (C) Interest Rate required for the Loan
• Unknown / Trying to Solve For:
  • How much is the original (D) Loan Amount aka what would somebody pay upfront for these future cash flows knowing they need to hit theire required interest rate.

Said another way: If I had B, C, D, I could use the PPMT and IPMT formulas to determine A. How Do I Determine D when having A, B, and C?

Greens are the variables and am solving for Orange:

 

[Cubist]

Just discount all the cashflows with the given interest rate to time 0 and sum them up?
Assuming you already know this, are you looking for a single formula that does this?

 

[baileyisnotreal]

This is right. Was in my own head. Thank you for sanity check.