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AleksandrR [38]
3 years ago
9

Eva picked 3 " #pounds of blueberries, Josh picked 2.5 pounds, and David picked 4 $ %pounds. If they place all the blueberries i

n one basket and then separate them so that they each take home the same amount of blueberries, how many pounds would each person take home?
Mathematics
1 answer:
yKpoI14uk [10]3 years ago
6 0
3.17 pounds a person
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Paul wants to buy a car. He needs to take out a loan for $7000. The car salesman offers him a loan with an interest rate of 8%,
Alisiya [41]

Answer:

a. It will take approximately 40 months

b. The total amount Paul has to pay is approximately $8,000

c. The amount Paul pays each month is approximately $316.59

d. The amount Paul has to pay is approximately $7,598.16

e. Lower monthly payment

f. Lower total payment amount (amount to be paid)

Step-by-step explanation:

a. The loan amount, PV = $7,000

The annual interest rate, r = 8%

Option 1; The amount of equal monthly payment to repay the loan = $200

Option 2; The number of equal monthly payment to repay the loan = 24

The formula for the present value of an annuity is given as follows;

PMT = \dfrac{\dfrac{r}{12}  \times PV}{1 - \left (1 + \dfrac{r}{12} \right)^{-n}}

Where;

PMT = The monthly payment

n = The number of months

Where PMT = $200, we have;

200 = \dfrac{\dfrac{0.08}{12}  \times 7,000}{1 - \left (1 + \dfrac{0.08}{12} \right)^{-n}}

1 - \dfrac{\dfrac{0.08}{12}  \times 7,000}{200}  = \left (1 + \dfrac{0.08}{12} \right)^{-n}

1 - \dfrac{7}{30}  = \dfrac{23}{30} =  \left ( \dfrac{151}{150} \right)^{-n}

-n = \dfrac{ ln \left(\dfrac{23}{30} \right)}{ln\left(\dfrac{151}{150} \right) } \approx -39.988

∴ The number of months it will take for Paul to repay the loan, n ≈ 39.988 ≈ 40 months

b. The total amount Paul has to pay, A = PMT × n

Therefore, b plugging in the values of PMT, and 'n', we get;

A ≈ $200 × 40 = $8,000

c. Using option 2, we have;

n = 24

Therefore;

PMT = \dfrac{\dfrac{0.08}{12}  \times 7,000}{1 - \left (1 + \dfrac{0.08}{12} \right)^{-24}} \approx 316.59

The monthly payment, PMT ≈ $316.59

d. The total amount Paul has to pay using option 2, A ≈ 316.59 × 24 = 7,598.16

The total amount Paul has to pay using option 2, A ≈ $7,598.16

e. A reason why Paul might choose option 1 is that option 1 offers lower monthly payment

f. A reason why Paul may choose option 2 is that option 2 offers a lower total amount that he has to pay.

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Answer:

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Step-by-step explanation:

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