Formulas and Functions

RATE
The RATE function returns the interest rate of an investment, loan, or annuity based
on a series of regular periodic cash ows (payments of a constant amount and all cash
ows at constant intervals) and a xed interest rate.
RATE(num-periods, payment, present-value, future-value, when-due, estimate)
 num-periods: The number of periods. num-periods is a number value and must be
greater than or equal to 0.
 payment: The payment made or amount received each period. payment is a
number value. At each period, an amount received is a positive amount and an
amount invested is a negative amount. For example, it could be a monthly loan
payment (negative) or the periodic payment received on an annuity (positive).
 present-value: The value of the initial investment, or the amount of the loan or
annuity. present-value is a number value. At time 0, an amount received is a positive
amount and an amount invested is a negative amount. For example, it could be an
amount borrowed (positive) or the initial payment made on an annuity contract
(negative).
 future-value: An optional argument that represents the value of the investment
or remaining cash value of the annuity (positive amount), or the remaining loan
balance (negative amount), after the nal payment. future-value is a number value.
At the end of the investment period, an amount received is a positive amount and
an amount invested is a negative amount. For example, It could be the balloon
payment due on a loan (negative) or the remaining value of an annuity contract
(positive).
 when-due: An optional argument that species whether payments are due at the
beginning or end of each period. Most mortgage and other loans require the rst
payment at the end of the rst period (0), which is the default. Most lease and rent
payments, and some other types of payments, are due at the beginning of each
period (1).
end (0 or omitted): Payments are due at the end of each period.
beginning (1): Payments are due at the beginning of each period.
 estimate: An optional argument specifying the initial estimate for the rate of return.
estimate is a number value and is either entered as a decimal (for example, 0.08) or
with a percent sign (for example, 8%). If omitted, 10% is assumed. If the default value
does not result in a solution, initially try a larger positive value. If this does not result
in an outcome, try a small negative value. The minimum value allowed is –1.
144 Chapter 6 Financial Functions