FVSCHEDULE

Returns the future value of a lump sum, with changing future interest rates.

Syntax:

FVSCHEDULE(principal, interestrates)

principal: the initial value of the lump sum.

interestrates: a range or array containing a schedule of interest rates which apply each period.

FVSCHEDULE calculates the future value by applying each interest rate in turn, and compounding. The formula is:

$p r in c i p a l * (1 + r a t e_{1}) * (1 + r a t e_{2}) * (1 + r a t e_{3}) * \dots$

where $r a t e_{i}$ is the $i^{t h}$ interest rate in interestrates.

Example:

FVSCHEDULE(1000, {.05, .06, .07})

returns 1,190.91, the future value of 1000 in 3 years time, where you believe the appropriate interest rates will be 5% in the first year, 6% in the second year and 7% in the third year.

Application:

Scenario: A small business is planning to invest a lump sum of $50,000 for a period of four years. The investment vehicle offers a variable interest rate that changes each year.

The interest rates are as follows:

Year 1: 5.00%
Year 2: 5.50%
Year 3: 6.00%
Year 4: 6.50%

The business wants to determine the future value of their $50,000 investment at the end of the four-year period.

To solve this, we can use the FVSCHEDULE function.

FVSCHEDULE Function Syntax:

FVSCHEDULE(principal, schedule)

principal: The present value of the investment, which is $50,000.
schedule: An array or range of interest rates for each period.

Here is the data organized in a table:

	Year	Interest Rate
	A	B
1	1	5.00%
2	2	5.50%
3	3	6.00%
4	4	6.50%

Applying the FVSCHEDULE function:

In a spreadsheet, you would input the following formula:

FVSCHEDULE(50000, {0.05, 0.055, 0.06, 0.065})

Note: In a spreadsheet, you would typically reference the cells containing the interest rates, for example, FVSCHEDULE(B2,C2:C5) where B2 is the principal and C2:C5 is the range of interest rates.

Calculation Breakdown:

The FVSCHEDULE function works by compounding the principal amount through each interest rate in the schedule.

End of Year 1: $50,000 * (1 + 0.05) = $52,500
End of Year 2: $52,500 * (1 + 0.055) = $55,387.50
End of Year 3: $55,387.50 * (1 + 0.06) = $58,710.75
End of Year 4: $58,710.75 * (1 + 0.065) = $62,526.95

Result:

The FVSCHEDULE function would return $62,526.95.

Conclusion:

This example demonstrates how the FVSCHEDULE function accurately calculates the future value of an investment with changing interest rates over a multi-year period. It provides a clear and precise way to project the growth of an investment, which is crucial for financial planning and decision-making for individuals and businesses alike.

Result:

$62,526.95