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)
Math question: What is the measure of angle DAB in a circle with central angle DOB measuring 120Β°?
+
What is the factored form of the quadratic equation 3x^2 + 7x + 2?
+
What is the simplified form of √(16) - √(9)?
+
New questions in Mathematics
Using a remarkable product you must factor the expression: f(x) =36x^2-324 and you are entitled to 5 steps
The gross domestic product the gdp for the United States in 2017 was approximately $2.05x10^3. If you wrote this number in standard notation , it would be 205 followed by how many zeros
2.5 / 21.85
(5u + 6)-(3u+2)=
Solve this mathematical problem if 3/5 of a roll of tape measures 2m. How long is the complete roll?
Find the derivatives for y=X+1/X-1
78 percent to a decimal
The durability of a tire of a certain brand is a Normal random variable with an average of 64,000 km and a standard deviation of 9,000 km. Assuming independence between tires, what is the probability that the 4 tires on a car will last more than 58,000 km?
A test has 5 multiple choice questions. Each question has 4 alternatives, only one of which is correct. A student who did not study for the test randomly chooses one alternative for each question.(a) What is the probability of him getting a zero on the test?(b) What is the probability of him getting a three or more? The maximum mark for the test is 5, with each question worth one point.
calculate the area in square units of A rectangle with length 6cm and breadth 5cm
Use the power rule for logarithms to solve the following word problem exactly. If you invest $1, 000 at 5% interest compounded annually, how many years will it take before you have $2,000?
Find the minimum value of the function y = -4 x3 + 60 x2 -252 x + 8 for values of x between x = 0 and x = 9 Enter the value of the function, not the value of x
MAKING AN ARGUMENT You use synthetic division to divide f(x) by (x βˆ’ a) and find that the remainder equals 15. Your friend concludes that f (15) = a. Is your friend correct? Explain your reasoning.
ind the z-score for which 72% of the distribution's area lies between -z and z. -1.7417, 1.7417 -1.1538, 1.1538 -1.0803, 1.0803 -2.826, 2.826
Given a circle π‘˜(𝑆; π‘Ÿ = 4 π‘π‘š) and a line |𝐴𝐡| = 2 π‘π‘š. Determine and construct the set of all centers of circles that touch circle π‘˜ and have radius π‘Ÿ = |𝐴𝐡|
What is the percentage of nitrogen abundance in copper dinatrate Cu(NO3)2
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?
the length of the fenced in area is to be 5 ft greater than the width and the total amount of fencing to be used is 89 ft find the width and length
Sin(5pi/3)
12[4 + (8 + 7) + 5]