In: Finance
Janet saves $3,000 a year at an interest rate of 4.2 percent. What will her savings be worth at the end of 35 years?
A. $229,317.82
B. $230,702.57
C. $230,040.06
D.
$234,868.92
E. $236,063.66
Solution:
The formula for calculating the Future value of savings at the end of n years is
= P *[ [ ( 1 + r ) n- 1 ] / r ]
Where P = Periodic Deposit 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 = $ 3,000 ; r = 4.2 % = 0.042 ; n = 35
Applying the above values in the formula we have:
= 3000 * [ [ ( 1 + 0.042 ) 35 - 1 ] / 0.042 ]
= 3000 * [ [ ( 1.042 ) 35 - 1 ] / 0.042 ]
= 3000 * [ [ 4.2205610 – 1 ] / 0.042 ]
= 3000 * [ 3.2205610 / 0.042 ]
= 3000 * 76.6800196
= 230040.0588
= $ 230040.06 ( when rounded off to two decimal places )
Thus the Solution is Option C. $ 230,040.06
Thus if Janet saves $3,000 a year at an interest rate of 4.2 percent her savings be worth $ 230,040.06 at the end of 35 years.
Note: The value of ( 1.042 ) 35 is calculated using the Excel formula =POWER(Number,Power)
=POWER(1.042,35)= 4.2205610