Effective Interest Tables

Lesson:

Interest tables are pre-calculated charts that help you solve time value of money problems quickly. Instead of doing complex calculations every time, you simply look up the answer. Think of them like a multiplication table, but for money growing over time.

These tables save you hours of calculation and reduce errors. Do note, however, that rounding and other issues often leave you with a handful of cents remaining after the loan has essentially been paid off. There are different ways to handle such remainders, but we'll use the easiest method of just tacking them on to the last payment.

Payments over time are often categorized in one of two ways:

Ordinary Annuities (Normal Annuities) - Payments occur at the end of each time period (such as each year).

Annuities Due - Payments occur at the start of each time period (such as each year). Yes, that means that the very first day a borrower receives an annuity due loan, he must make a payment.

Answer:

Explanation:

1. OK, First, write down the interest rate to use. We'll need it later.
   INTEREST RATE = 6%
2. Next, create the header for the effective interest table. It will always have the same columns, so it is helpful to memorize them.

   Year	Lease Payment	Interest	Lease Reduction	Lease Liability

3. As soon as we enter into a lease, we have a liability on our books. Our liability is the present lease value of all payments:
   $5,667
4. Let's fill in our initial row with our lease liability. We'll worry about payments and interest later.

   Year	Lease Payment	Interest	Lease Reduction	Lease Liability
   Lease Initiation	$0.00	$0.00	$0.00	$5,666.80

5. Now we move to the next row. Since the payments are annuity due, each subsequent row will be the start of the lease year, beginning with the very first day of the lease.
6. The lease payment is always the same, and it was already given to us:
   $2,000.00
7. The interest rate was given as 6% per year, but we need to calculate the dollars of interest, not the percentage of interest.
8. The interest rate was given as 6% per year. Since we just started the lease today, we didn't accumulate any interest. If we had, we would have taken the lease liability from the previous row and multiplied it by our interest rate (6%).
9. We made a payment, but how much of it reduced the principle of our loan? Let's take the difference from our payment and interest paid, and record it under lease reduction.
   LEASE REDUCTION = LEASE PAYMENT - INTEREST
10. And finally we enter the remaining lease liability which we get from subtracting the amount we paid against principle from the previous row's lease liability.
    CURRENT LEASE LIABILITY = PREVIOUS LEASE LIABILITY - CURRENT LEASE REDUCTION
11. With a bit of luck, our table should look like this.

    Year	Lease Payment	Interest	Lease Reduction	Lease Liability
    Lease Initiation	$0.00	$0.00	$0.00	$5,666.80
    Start of year #1	$2,000.00	$0.00	$2,000.00	$3,666.80

12. Now we keep repeating the process until our lease liability is equal to zero. Remember that our liability should never go below zero, so we may have to reduce the lease payment in the final year, so that the lease liability hits exactly zero.

    Year	Lease Payment	Interest	Lease Reduction	Lease Liability
    Lease Initiation	$0.00	$0.00	$0.00	$5,666.80
    Start of year #1	$2,000.00	$0.00	$2,000.00	$3,666.80
    Start of year #2	$2,000.00	$220.01	$1,779.99	$1,886.81
    Start of year #3	$2,000.02	$113.21	$1,886.81	$0.00