Valuing a Loan with a Grace Period and Changing Monthly Rates

Summary

The document presents a cash-flow valuation problem for a loan with an initial grace period, a period of fixed payments, and then an unknown regular payment. Monthly interest rates rise across the three years of the term. The task is to find the payment that settles the balance, given the loan principal and earlier payments, and the questioner compares a spreadsheet-style equation with a textbook answer.

The attempted method selects month six as a focal date and accumulates or discounts each cash flow to that date. The document does not include a worked correction or explain the discrepancy, so it cannot establish the stated textbook payment or diagnose which timing convention is wrong. It illustrates the need to align every payment and rate period consistently when valuing cash flows under changing rates. This is general financial mathematics rather than a trading strategy, and the example leaves ambiguity about payment timing and how the annual rate schedule applies at period boundaries.

Key ideas

• A loan with changing rates can be valued by moving each cash flow to a common focal date.
• The unknown installment is found by equating the present or accumulated values of the loan and payments.
• Grace periods affect both the balance and the timing of later payments.
• The document gives an attempted equation but no worked resolution of its disagreement with the textbook figure.

Tags

# Annuities problem


# Annuities problem












First problem is like this:

loan amount: 20,000,000.00

First six months: There is no payment but there are interest (grace period)

Next six months: payment of 600,000.00

Since 13 month: payment of R

Term: 3 years

Interest rate:

First year: 1% effective monthly

Second year:1.5% effective monthly

Third year: 2% effective monthly

Find R value

Answer from textbook 954,066.98

My attempt: I put focal date on month six, then i move 20M to focal date and late i tried to move all payments to my focal date

https://www.wolframalpha.com/input/?i=solve+21020201%3D600000%281-%281%2B0.01%29^-6%29%2F0.01%2Bx%28%281-%281%2B0.015%29^-6%29%2F0.015%29*%281%2B0.015%29^-6%2Bx*%28%281-%281%2B0.02%29^-12%29%2F0.02%29*%281%2B0.02%29^-18

But i guess that was, 'cause wolfram answer is really far from textbook

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.