`find the amount of each payment into a sinking fund so that a total of $6000 can be accumulated, with 9 annual payments and an interest rate of 4% compounded annually.`

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Answer from Sia

Posted about 1 month ago

Solution by Steps

step 1

We start with the equation for the sinking fund: $P \times \frac{(1 - (1 + 0.04)^{-9})}{0.04} = 6000$

step 2

Rearranging the equation to solve for $P$: $P = 6000 \times \frac{0.04}{(1 - (1 + 0.04)^{-9})}$

step 3

Calculating $(1 + 0.04)^{-9}$: $(1 + 0.04)^{-9} \approx 0.6651$

step 4

Substituting back into the equation: $P = 6000 \times \frac{0.04}{(1 - 0.6651)}$

step 5

Simplifying further: $P = 6000 \times \frac{0.04}{0.3349} \approx 806.958$

Answer

The amount of each payment into the sinking fund is approximately $806.96

Key Concept

Sinking Fund Calculation

Explanation

The sinking fund formula helps determine the regular payment needed to accumulate a specific amount over time, considering interest rates. In this case, with 9 payments and a 4% interest rate, the calculated payment is approximately $806.96.

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