Determine the future value of Rs.1000 compounded continuously for 5 year on the interest rate of 12 percent per year and contrast it along with annual compounding.
Solution:
FV_{=5} = PVe^{N(APR)}
= 1000 * 2.71828
= 1000 * 2.71828^{.60}
= 1000 * 1.82212
FV_{=5} = PV (1 + k)^{n}
= 1000 (1 + .12)^{5}
= 1000 (1.7623)
= 1762.3
From this illustration you can very well notice the effects of extreme frequency of compounding.
until now in our discussion we have supposed that the interest rate is going to stay the same over the life of the investment, although now a days we are witnessing an raised volatility in interest rates as a effect of that the financial instruments are designed in a manner that interest rates are benchmarked to a specific variable and along with the change in which variable the interest rates also change consequently.
In that case the Future Value is calculated by this equation:
FV_{n} = PV(1 + k_{1} ) (1 + k_{2} ) (1 + k_{3} ) + ... (1 + k_{n} )
Here k_{n} is the interest rate for period n.