Calculating Interest Rates with Microsoft Excel

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The Rate function calculates the interest rate implicit in a set of loan or speculation terms
given the number of periods (months, quarters, years or whatever), the cost per period, the present value, the time to come value, and, optionally, the type-of-annuity switch, and also optionally, an interest-rate guess.

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If you set the type-of-annuity switch to 1, Excel assumes payments occur at the beginning
of the period, following the annuity due convention. If you set the annuity switch to 0 or
you omit the argument, Excel assumes payments occur at the end of the duration following
the ordinary annuity convention.

The function uses the following syntax:

Rate (nper, pmt, pv, fv, type, guess)

As one example, suppose you want to imagine the implicit interest rate on a car lease for a ,000 car that requires five years of 0-a-month payments (occurring as an annuity due) and also a
,000 balloon payment. To do this, assuming you want to start with a guess of 10%, you
can use the following formula:

=Rate(5*12,-250,20000,-15000,1)

The function returns the value .95%, which is a monthly interest rate of just less than 1%.
If you annualize this monthly rate by multiplying it by 12, you get an equivalent annual
interest rate of 11.41%.

As other example, suppose you want to imagine the implicit interest rate on a 0,000 real estate mortgage that requires thirty years of 00-a-month payments (occurring as an ordinary annuity) but (thankfully) no balloon payment. To do this, assuming you want to start with a guess of 10%, you can use the following formula:

=Rate(30*12,-2000,300000)

The function returns the value .59%, which is a monthly interest rate of slightly more than half a percent.
If you annualize this monthly rate by multiplying it by 12, you get an equivalent annual
interest rate of 7.0203%.

A final point: Excel solves the Rate function iteratively starting with the guess seminar you provide.
(If you don't furnish this optional argument, Excel uses 10%.) If Excel can't solve the Rate seminar within 20 attempts, it returns the #Num! error. You can try a different guess argument, which may help because you're telling Excel to begin its quest from a different (hopefully closer) starting point.

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