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Find the amount of each payment to be made into a sinking fund which earns 5â% compounded quarterly and produces â$55 comma 000 at the end of 4.5 years. Payments are made at the end of each period. The payment size is $?

Respuesta :

Answer:

$2743.66

Step-by-step explanation:

Data provided in the question:

Interest rate = 5%

Future value = $55,000

Time, t = 4.5 years

Now,

Since the interest is compounded quarterly

therefore,

Number of periods in a year = 4

Interest rate per period = 5% ÷ 4 = 1.25% = 0.0125

Total number of periods in 4.5 years = 4.5 × 4 = 18

also,

PMT = Future value × [ r × (( 1 + r )ⁿ - 1)⁻¹ ]

therefore,

PMT = $55,000 × [ 0.125 × ( ( 1 + 0.0125 )¹⁸ - 1 )⁻¹ ]

or

PMT = $55,000 × 0.0498

or

PMT = $2743.66

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