Question

A company estimates that it will need $138,000 in 11 years to replace a computer. If it establishes a sinking fund by making fixed monthly payments into an account paying 5.1 % compounded​ monthly, how much should each payment​ be?

Answer 1

The amount is computed as shown below:

Future value = Monthly payment x [ [ (1 + r)ⁿ – 1 ] / r ]

r is computed as follows:

= 5.1% / 12 (Since the interest is compounded monthly, hence divided by 12)

= 0.425% or 0.00425

n is computed as follows:

= 11 x 12 (Since the interest is compounded monthly, hence multiplied by 12)

= 132

So, the amount will be as follows:

$ 138,000 = Monthly payment x [ [ (1 + 0.00425)¹³² - 1 ] / 0.00425 ]

$ 138,000 = Monthly payment x 176.5510772

Monthly payment = $ 138,000 / 176.5510772

Monthly payment = $ 781.64 Approximately

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