Future value of 1000ドル at an effective interest rate of 5% after 3 compounding periods:

Present value of 1000ドル at the same interest rate of 5% after 3 compounding periods:

Present value at 6% of a 12-period annuity with payments of 100ドル:

Future value at 6% of a series of cash flows occurring at regular intervals:

Present value of an amount paid at time 10 using a term structure of interest rates:

Future value of 1000ドル using a nominal rate of 5% with quarterly compounding:

Symbolic time value computations:

Time value computation using a rate schedule:

Present value using a schedule of rates effective at the specified times:

Future value using a schedule of rates over irregular time intervals:

Time value based on a force of interest function:

Valuation of cash flows:

A symbolic cash flow computation:

Valuation of annuities:

A symbolic annuity calculation:

Number of periods required to grow 1000ドル to 3000ドル at a 6% interest rate:

Symbolic solution for the number of periods:

Solve for the interest rate:

Solve an annuity calculation for the payment amount:

Compute the future value after three time periods using a force of interest :

An annuity with a continuous payment flow can be coupled with a force of interest specification:

Future value in three years' time of 1000ドル invested on January 1, 2010, at 7.5%:

Hours, minutes, and seconds can be given in date specifications:

Future value after 5 periods using a schedule of rates over unit time intervals:

Rates can be given as a TimeSeries :

Find the amount that must be invested at a rate of 9% per year in order to accumulate 1000ドル at the end of 3 years:

Find the accumulated value of 5000ドル over 5 years at 8% compounded quarterly:

Find how much time it will take 1000ドル to accumulate to 1500ドル if invested at 6%, compounded semiannually:

Find the future value of 1 at the end of n years if the force of interest is , where t is time:

Find an expression for the accumulated value of 1000ドル at the end of 15 years if the effective interest rate is r₁ for the first 5 years, r₂ for the second 5 years, and r₃ for the third 5 years:

If you invest 1000ドル at 8% per year compounded quarterly, find how much can be withdrawn at the end of every quarter to use up the fund exactly at the end of 10 years:

Find the rate, compounded quarterly, at which 16000ドル is the present value of a 1000ドル payment paid at the end of every quarter for 5 years:

Find the accumulated value of a 10-year annuity of 100ドル per year if the effective rate of interest is 5% for the first 6 years and 4% for the last 4 years:

Find the net present value of a 1000ドル initial investment producing future incoming cash flows:

Find the internal rate of return of an investment with regular cash flows:

In return for receiving 600ドル at the end of 8 years, a person pays 100ドル immediately, 200ドル at the end of 5 years, and a final payment at the end of 10 years. Find the final payment amount that will make the rate of return on the investment equal to 8% compounded semiannually:

Payments of 100,ドル 200,ドル and 500ドル are due at the end of years 2, 3, and 8, respectively. Find the point in time where a payment of 800ドル would be equivalent at 5% interest:

Another method to solve the problem above:

Find the effective rate of interest at which the present value of 2000ドル at the end of 2 years and 3000ドル at the end of 4 years will be equal to 4000ドル:

Since a loan's balance at any time is equal to the present value of its remaining future payments, Annuity can be used to create an amortization table:

Graph the principal payoff over time:

Present value using a schedule of rates over irregular time intervals:

This is equivalent to:

Use Plot and Plot3D to show the dependencies of an annuity on a set of parameters:

Dependence on interest rate:

Dependence on payment growth rate:

Use Plot3D to view the interest rate/growth rate landscape:

When finding interest rate solutions to long-term or high-frequency annuities or bonds, FindRoot may be needed instead of Solve :

In order for TimeValue to determine if there are enough rates in a schedule to reach the valuation period, the valuation period must be numeric:

Input numeric valuation period:

Specifying rates by a TimeSeries requires the first time to be 0:

Shift the time series:

Use Manipulate to explore the various dependencies a series of cash flows has on a set of variables: