Third time posting. Explain it too
2 answers:
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Given:
m is directly proportional to the cube of h.
m = 525 when h= 5.
To find:
The equation connecting m and h.
Solution:
m is directly proportional to the cube of h.
...(i)
Where, k is the constant of proportionality.
Putting m = 525 and h= 5, we get
Putting k=105 in (i), we get
Therefore, the required equation is .
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;
Where;
PMT = The monthly payment
n = The number of months
Where PMT = $200, we have;
∴ 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;
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.