Question

In: Finance

You want to have $54,000 in your savings account 5 years from now, and you're prepared...

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

Multiple Choice

$10,800.00
$3,941.97
$9,334.06
$3,942.02
$13,155.56

Expert Solution

Solution:

The formula for calculating the Future value of equal annual deposits 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 $ 9,334.06 in order receive $ 54,000 in 5 years assuming the account pays an annual interest of 7.3 % .

The solution is option 3 = $ 9,334.06

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

=POWER(1.073,5)= 1.422324

jeff jeffy answered 2 years ago

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