Question

Future Vaule of Multiple Annunities

Answer 1

Multiple Annuity

Annuity means fixed sum payable periodically. Multiple annuities means 2 or more of such annuity. Let us understand it with an example:

a. Annuity: Mr A has to pay $ 100 every year end for next 10 years.

b. Multiple annuity: Mr A has to pay $100 every year for 5 years thereafter will pay $50 for next 5 years.

Future Value (FV = Amount (1+r)^n where r= rate of interest / 100 & n = period )

FV means value of an item at specified future date. Eg: Say $100 loan taken today if needs to be paid at 3% interest p.a then post 1 year you would be required to pay $103. i.e FV= 100(1+.03)^1

Future value of multiple annuities

Having understood FV and multiple annuities seperately, I am sure you would be able to connect both the concepts.

It means future value of 2 or more annuities at end of specified period. Let us understand it with an example.

Say Mr. A has to pay Mr. B $100 beginning of every year for 2 years, post which he has to pay $50 for next 2 years. What is the value of such annuity at 4th year end if interest charged is 10%.  

Calculation : Induvidually calculate future value of each payments at 4th year end and add all of them together.

a. Payment 1 of $ 100 : FV= 100 * (1+0.1)^4 i.e 146.41

b. Payment 2 of $ 100: FV= 100 * (1+0.1)^3 i.e 133.1

c. Payment 3 of $ 50 : FV= 50 * (1+0.1)^2 i.e 60.5

d. Payment 4 of $ 50: FV= 50 * (1+0.1)^1 i.e 55

Thus FV of multiple annuities is $ 395/-. ( Adding all the 4 )

The above calculation made is just to clear your concepts, this can be easily solved by using annuity table.