Question

"What is the future value of an ordinary $1,000 annuity payment over six years if interest rates are 6% (assume annual compounding)?"

		"$6,000.00 "
		"$6,975.32 "
		"$4,917.32 "
		"$9,675.32 "
		Not possible to compute with the data provided

Answer 1

Solution:

The formula for calculating the Future value of an ordinary annuity at the end of ' n ' years is

= P * [ [ ( 1 + r ) ⁿ - 1 ] / r ]

Where

P = Annuity payment i.e., Fixed amount of Annual deposit ; r = rate of interest   ; n = no. of years ;

A per the information given in the question we have

P = $ 1,000    ; r = 6 % = 0.06   ;   n = 6    ;

Applying the above values in the formula we have:

= 1,000 * [ [ ( 1 + 0.06 ) ⁶   - 1 ] / 0.06 ]                      

= 1,000 * [ [ ( 1.06 ) ⁶   - 1 ] / 0.06 ]

= 1,000 * [ [ 1.418519 – 1 ] / 0.06 ]

= 1,000 * [ 0.418519 / 0.06 ]

= 1,000 * 6.975319

= 6,975.3190

= $ 6,975.32 ( when rounded off to two decimal places )

Thus the future value of an ordinary $ 1,000 annuity payment over six years if interest rates are 6% (assume annual compounding) = $ 6,975.32

The Solution is Option 2. $ 6,975.32

Note: The value of ( 1.06 ) ⁶   is calculated using the Excel function =POWER(Number,Power)

=POWER(1.06,6)= 1.418519