Future Value of Single Cash Flow for Multiple-Period Investment with Multiple Interest Rates

Future Value of Single Cash Flow for Multiple-Period Investment with  Multiple Interest Rates

Future Value with a Single Cash Flow:

Time value of money for a single cash flow is a cash inflow or outflow that investors or lenders received from or paid to once respectively for specific periods.

Future value (FV) refers to the amount of money an investment or present value (PV) will grow for specific periods of time at specific interest rate.

Future Value = Present Value + all earned interests

Multiple-Period Investment:

Multiple-period investment may be investment for more than one year. Term multiple-period can refer to more than one day or one month investment, so it isn’t always more than one year investment.

If period investments are based on one day, one month or one year etc., so discount rates are based on one day, one month or one year respectively.

Definition of Multiple Interest Rates :

We can calculate future value with different interest rates or growth rates for different periods.

 Formula of Future Value with multiple discount rates for Multiple-Period Investment:

FV = PV(1 + r₁ ) (1 + r₂) (1 + r₃) . . . (1 + r_t)

where

PV: Present Value or principal is worth today

FV: Future value is worth in the future

r1,r2,r3…,r_t : Interest rate, rate of return, or discount rate per period  (but not always one year ) for period 1, 2, 3,…,t respectively

Question

 Suppose an investment of $20,000 will be paid 9% during the first year, 10% during the second year and 11% during the third year.

What is the future value of investment for three years?

Solution

First Method

FV(Year3)=$20,000 x (1+9%)x(1+10%)x(1+11%)=$26,618

Second Method

FV(Year1)=$20,000 x (1+9%)=$21,800

FV(Year2)= FV(Year1) x (1+10%)=$21,800 x (1+10%)=$23,980

FV(Year3)=FV(Year2) x ( 1+11%)=$23,980 x (1+11%)=$26,618