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 amount of periods (months, quarters, years or whatever), the payment per period, the present value, the future 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 lowly annuity convention.

The function uses the following syntax:

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

As one example, suppose you want to intuit 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 an additional one example, suppose you want to intuit the implicit interest rate on a 0,000 real estate mortgage that requires thirty years of 00-a-month payments (occurring as an lowly 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 beginning with the guess discussion you provide.
(If you don't contribute this optional argument, Excel uses 10%.) If Excel can't solve the Rate discussion within 20 attempts, it returns the #Num! error. You can try a dissimilar guess argument, which may help because you're telling Excel to begin its search from a dissimilar (hopefully closer) beginning point.

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