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Suppose you want to save in order to purchase a new boat. Take the APR to be 6.0%.

You want to have $15,000 toward the purchase of a boat in three years. How much do you need to deposit each month? (Round your answer to the nearest cent.)

Respuesta :

Answer:

Amount deposit each month = $365.26

Step-by-step explanation:

Given:

Amount deposit = $15,000

Rate = 6% = 6% / 12 = 0.005

Number of time = 3 x 12 = 36

Find:

Amount deposit each month

Computation:

Amount deposit each month = [(15,000) x 0.005]/[(1.005){(1.005)³⁶-1}]

Amount deposit each month = $365.26

The amount needed to be deposited each month is;

P ≈ $393.23

We are given;

APR = 6% = 0.06

Total accumulated amount; A = $15000

number of years; n = 3 years

To calculate the amount needed to be deposited each month, we will use the formula;

A = [P(1 + APR/12)¹²ⁿ - 1)] ÷ (APR/12)

Plugging in the relevant values gives;

15000 = [P(1 + (0.06/12))⁽¹²*³⁾ - 1] ÷ (0.06/12)

Rearrange to get;

[P(1 + (0.06/12))³⁶ - 1] = 15000 × 0.06/12

⇒ [P(1 + 0.005)³⁶ - 1] = 75

⇒ P(0.19073) = 75

⇒ P = 75/0.19073

⇒ P ≈ $393.23

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