| LO4 – Describe and calculate the effective interest method of amortization and explain how this differs from the straight-line amortization method. |
Interest is the time value of money. If you borrow $1 today for one year at 10% interest, its future value in one year is $1.10 ($1 x 110% = $1.10). The increase of 10 cents results from the interest on $1 for the year. Conversely, if you are to pay $1.10 one year from today, the present value is $1 – the amount you would need to invest today at 10% to receive $1.10 in one year’s time ($1.10/110% = $1). The exclusion of applicable interest in calculating present value is referred to as discounting.
If the above $1.10 amount at the end of the first year is invested for an additional year at 10% interest, its future value would be $1.21 ($1.10 x 110%). This consists of the original $1 investment, $.10 interest earned in the first year, and $.11 interest earned during the second year. Note that the second year’s interest is earned on both the original $1 and on the 10 cents interest earned during the first year. This increase provides an example of compound interest – interest earned on interest.
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The following formula can be used to calculate this: |
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F = P x (1+i)n |
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where F = future value, P = present value, i = the interest rate, and n = number of periods. |
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Substituting the values of our example, the calculation would be, F = $1[(1 + .1)2], or $1.21.
If the future value of today’s $1 at 10% interest compounded annually amounts to $1.21 at the end of 2 years, the present value of $1.21 to be paid in 2 years, discounted at 10%, is $1. The formula to calculate this is just the inverse of the formula shown above, or
Substituting the values of our example,
That is, the present value of $1.21 received two years in the future is $1. The present value is always less than the future value, since an amount received today can be invested to earn a return (interest) in the intervening period. Calculating the present value of amounts payable or receivable over several time periods is explained more thoroughly below.
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