Question

When purchasing a car and 3 documents worth $15,000 will be paid each to be paid in months 2, 4 and 6. If you wish to pay in 2 installments equal, in months 4 and 8. What should be the amount of these payments? Consider that money changes at a rate of 35% compounded semiannually monthly.

283

likes
1413 views

Answer to a math question When purchasing a car and 3 documents worth $15,000 will be paid each to be paid in months 2, 4 and 6. If you wish to pay in 2 installments equal, in months 4 and 8. What should be the amount of these payments? Consider that money changes at a rate of 35% compounded semiannually monthly.

Expert avatar
Brice
4.8
113 Answers
To solve this problem, we need to find the equivalent value of three payments of $15,000 each, due in months 2, 4, and 6, and then determine the size of two equal payments in months 4 and 8.

### Step 1: Calculate the monthly interest rate
Given a 35% annual interest rate compounded semiannually:
- Semiannual rate = 35% / 2 = 17.5% per half year.

To convert a semiannual rate to a monthly rate when compounded semiannually:
\left(1 + \text{Semiannual rate}\right)^{\left(\frac{1}{6}\right)} - 1

Calculating it:
\left(1 + 0.175\right)^{\left(\frac{1}{6}\right)} - 1 = \left(1.175\right)^{\left(\frac{1}{6}\right)} - 1 \approx 0.0273 \text{ or } 2.73\% \text{ per month}

### Step 2: Calculate the present value of payments at month 4
- **Month 2**: $15,000 due in 2 months discounted to month 4:
PV_{\text{month 2 to 4}} = \frac{15000}{(1.0273^2)} = \frac{15000}{1.0559} \approx 14212.48
- **Month 4**: $15,000 due in 0 months
PV_{\text{month 4}} = 15000
- **Month 6**: $15,000 due in 2 months forward from month 4:
PV_{\text{month 6 to 4}} = \frac{15000}{(1.0273^2)} = \frac{15000}{1.0559} \approx 14212.48

Total present value at month 4:
PV_{\text{total}} = 14212.48 + 15000 + 14212.48 \approx 43424.96

### Step 3: Calculate the amount of each of the two equal payments in months 4 and 8
Let x be the payment amount in months 4 and 8.

x + \frac{x}{(1.0273^4)} = 43424.96
x + \frac{x}{1.1145} = 43424.96
x (1 + \frac{1}{1.1145}) = 43424.96
x (1.7933) = 43424.96
x = \frac{43424.96}{1.7933} \approx 24223.72

### Answer:
Each of the two equal payments to be made in months 4 and 8 should be approximately $24,223.72 to cover the equivalent value of the three payments worth $15,000 each due in months 2, 4, and 6, considering the given interest rate.

Frequently asked questions (FAQs)
What is the area of a triangle with side lengths 8, 10, and 12 using Heron's Formula?
+
What is the value of f(x) when f(x) is a constant function and c represents the constant value? (
+
What is the sum of the interior angles in a dodecagon?
+
New questions in Mathematics
A normal random variable x has a mean of 50 and a standard deviation of 10. Would it be unusual to see the value x = 0? Explain your answer.
Solution to the equation y'' - y' - 6y = 0
-11+29-18
what is 3% of 105?
3(4x-1)-2(x+3)=7(x-1)+2
What will be the density of a fluid whose volume is 130 cubic meters contains 16 technical units of mass? If required Consider g=10 m/s2
9b^2-6b-5
Emma is on a 50 m high bridge and sees two boats anchored below. From her position, boat A has a bearing of 230° and boat B has a bearing of 120°. Emma estimates the angles of depression to be about 38° for boat A and 35° for boat B. How far apart are the boats to the nearest meter?
determine the polynomial F of degree 2 that interpolates. f at points (0;1) (2;5) (4;6). calculate F(0.8). Note: Using the polynomial expression with difference operator.
The ninth term of a given geometric progression, with reason q , is 1792, and its fourth term is 56. Thus, calculate the fourth term of another geometric progression, whose ratio is q +1 and whose first term is equal to the first term of the first P.G. described.
The two sides of the triangle are 12 cm and 5 cm, and the angle between the sides is 60°. Cover the area of ​​the triangle!
Find the zero of the linear function 8x + 24 = 0
A natural gas company has a fixed rate of 1,320 pesos plus 1,590 pesos per cubic meter of gas consumed monthly per customer. Indicate the cost function to determine the value in pesos of the cubic meters of gas consumed in a month per customer. How much did a customer who consumed 18 cubic meters of gas pay? If a customer paid 34,710 pesos, how many cubic meters of gas did he consume?
Find the area of a triangle ABC when m<C = 14 degrees, a = 5.7 miles, and b = 9.3 miles.
Solve for B write your answer as a fraction or as a whole number. B-1/7=4
2+2020202
did an analysis of dropout from the nursing faculty at the Universidad Veracruzana. With a poblation of 122 students, it turned out that according to the gender data, the female sex predominates with 82%, and the male sex male is found with 12%. The main factors why students drop out are, first of all, "Not "re-enrolled" at 49%, second place "Personal reasons" at 20%, third place "change of school" in 11%, "lack of documents" and "economic reasons" in 7%, change of residence and lack of social service in 3%. Of this sample, how many students dropped out for other reasons?
Find the orthogonal projection of a point A = (1, 2, -1) onto a line passing through the points Pi = (0, 1, 1) and P2 = (1, 2, 3).
x(squared) -8x=0
To apply a diagnostic test, in how many ways can 14 students be chosen out of 25? if the order does not matter