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 + k_{1} ) (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