Question

Part of the income that a machine generates is put into a sinking fund to replace the machine when it wears out. If ​$2,000 is deposited annually at 8​% ​interest, how many years must the machine be kept before a new machine costing ​$55,000 can be​ purchased?

Answer 1

Solution :-

Amount Required = $55,000

Annual Deposit = $2,000

Rate of annual Interest = 8%

Now as per data given ,

$55,000 = $2,000 * FVAF ( 8% , n )

27.5 = [ ( 1 + 0.08)ⁿ - 1 ] / 0.08

(1.08)ⁿ - 1 = 2.20

(1.08)ⁿ = 3.20

Take log Both sides

n Log ( 1.08 ) = Log ( 3.20 )

n = 0.50515 / 0.033424

n = 15.114 Years

Therefore  the machine must be kept before a new machine costing ​$55,000 can be ​purchased = 15.114 Years

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