You want to have $54,000 in yo

You want to have $54,000 in your savings account 5 years fromnow, and you’re prepared to make equal annual deposits into theaccount at the end of each year. If the account pays 7.3 percentinterest, what amount must you deposit each year?

Multiple Choice

  • $10,800.00

  • $3,941.97

  • $9,334.06

  • $3,942.02

  • $13,155.56

Answer:

Solution:

The formula for calculating the Future value of equal annualdeposits at the end of ‘n’ years is

FV = P * [ [ ( 1 + r ) n – 1 ] / r ]

Where P = Equal Annual deposit   ;    r= rate of interest   ; n = no. of years ;

A per the information given in the question we have

FV = $ 54 ,000    ; r = 7.3 % = 0.073  ;   n = 5 Years   ; P = To find   ;

Applying the above values in the formula we have:

$ 54,000 = P * [ [ ( 1 + 0.073 )5 – 1 ] / 0.073 ]

$ 54,000 = P * [ [ ( 1.073 )5   – 1 ] /0.073 ]

$ 54,000 = P * [ [ 1.422324 – 1 ] / 0.073 ]

$ 54,000 = P * [ 0.422324 / 0.073 ]

$ 54,000 = P * 5.785263

P = $ 54,000 / 5.785263

P = $ 9,334.060610

P = $ 9,334.06 ( when rounded off to the nearest cent)

Thus the amount to be deposited each year is $ 9,334.06in order receive $ 54,000 in 5 years assuming the account pays anannual interest of 7.3 % .

The solution is option 3 = $ 9,334.06

Note: The value of ( 1.073 ) 5 iscalculated using the Excel function =POWER(Number,Power)

=POWER(1.073,5)= 1.422324


 
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