Notice an Rs.50, 000 investment in a one year fixed deposit and rolled over yearly for the subsequently two years.  The interest rate for the primary year is 5 percent  yearly and the expected interest rate for the subsequently two years are 6 percent  and 6.5 percent  respectively compute the future value of the investment after 3 years and the average annual interest rate.

Solution:

FV = PV (1 + k₁ ) (1 + k ₂ ) (1 + k ₃ )

= 50,000 (1 + .05) (1 + .06) (1 + .065)

= 59,267.25

Average annual interest rate

.05 +.06 + .065/3

 = .58333 (wrong)

 Already we know the values of FV, PV and n. The average yearly interest rate would be as:

k = ⁿ√(FV/PV)

= ³√(59267.25/50,000)

= ³√(1.185345)

= 5.8315%

= it is equivalent to

k = ³√((1 + .05) (1 + .06) (1 + .065)  - 1)

=5.8315