RRI

Returns an equivalent interest rate when an investment increases in value.

Syntax:

RRI(numperiods, presentvalue, futurevalue)

numperiods: the number of periods in the term.

presentvalue: the value at the start of the term.

futurevalue: the value at the end of the term.

RRI calculates the fixed interest rate needed, so that presentvalue invested for numperiods (and compounded each period) is worth futurevalue at the end of the term. RRI returns a fixed interest rate which applies to each period.

The underlying equation is:

$p rese n t v a l u e * (1 + RR I)^{n u m p er i o d s} = f u t u re v a l u e$

Example:

RRI(8, 1000, 1600)

returns approximately 6.05%. You invest $1,000, and receive $1,600 after 8 years. If you had instead invested that sum in a fixed rate interest account, with annually compounding interest, the account would have needed to pay 6.05% to gain the same value.

Application:

Analyzing Investment Performance

Imagine you invested in a mutual fund and want to understand its average annual return. You know your initial investment, the current value, and how long you've held the investment.

Initial Investment (Present Value, PV): $10,000
Current Value (Future Value, FV): $15,000
Investment Period (Nper): 5 years

You want to find out the constant annual interest rate that would have been required for your $10,000 to grow to $15,000 over those 5 years, assuming the interest was compounded annually.

Using the RRI Function

The RRI function syntax is:

RRI(nper, pv, fv)

In this case, the formula would be:

RRI(5, 10000, 15000)

The function would return the result, which you can then format as a percentage. The result would be approximately 8.45%.

This means that your investment grew at an average rate of 8.45% per year, compounded annually.

Example Table

The following table demonstrates the calculation for this scenario and a few others.

	Description	Nper (Years)	PV (Initial Value)	FV (Final Value)	RRI (Annual Rate)
	A	B	C	D	E
1	Mutual Fund	5	$10,000.00	$15,000.00	8.45%
2	Retirement Fund	20	$50,000.00	$200,000.00	7.18%
3	Savings Account	3	$5,000.00	$6,000.00	6.27%
4	Home Value	10	$300,000.00	$450,000.00	4.14%

As you can see from the table, the RRI function allows you to quickly compare the performance of different investments or assets on an "apples-to-apples" basis, even if they have different starting values, ending values, and investment periods.