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 formula to find the median of a data set with an odd number of elements?Answer: The median of a data set with an odd number of elements can be found by arranging the data in ascending order and selecting the middle value.
+
Question: Find the cube root of a number x, such that the cube root function has a vertical stretch of 2 and a horizontal shift 3 units to the right.
+
What is the equation of a hyperbola with a vertical transverse axis, center (0,0), vertices at (0,2) and (0,-2), and foci at (0,3) and (0,-3)?
+
New questions in Mathematics
2(2+2x)=12
5 squirrels were found to have an average weight of 9.3 ounces with a sample standard deviation is 1.1. Find the 95% confidence interval of the true mean weight
1 plus 1
How long will it take for $900 to become $5000 at an annual rate of 11.15% compounded bimonthly?
If you randomly selected one person from the 900 subjects in this study, what is the probability that the person exhibits the minimum BMI?
15/5+7-5
I want you to solve this problem as a grade sixth pupil in primary school: 8 Pigs ate 6 bags of fee in 20 days. How long will it take 10 pigs to eat 15 bags of feed eating at the same rate?
find f(x) for f'(x)=3x+7
. What will be the osmotic pressure of a solution that was prepared at 91Β°F by dissolving 534 grams of aluminum hydroxide in enough water to generate 2.784 ml of solution.
using the math and science known about the jefferson river bridge Find a truss in use and develop a load diagram. Use a load of 50 lb on each joint along the bottom of the truss for a truss that actrs as a bridge and along the top joints for a truss that acts as a roof
How to do 15 x 3304
7=-4/3y -1
A teacher has 25 red and yellow counters altogether. She has 4 times as many red counters than yellow counters. How many yellow counters does the teacher have?
48 kg of 30% sulfuric acid in a mixture of 10% and 40% sulfuric acid arose. How many kilograms were each of the original solutions?
Find the area of a triangle ABC when m<C = 14 degrees, a = 5.7 miles, and b = 9.3 miles.
Pablo has a balance of $440,000 and 2/5 of the money is used to pay bills. How much money do you have left after paying the bills?
(6Β²-14)Γ·11β€’(-3)
A factory produces glass for windows. The thickness X of an arbitrarily selected pane of glass is assumed to be Normally distributed with expectation ΞΌ = 4.10 and standard deviation Οƒ = 0.04. Expectation and Standard deviation is measured in millimeters. What is the probability that an arbitrary route has a thickness less than 4.00 mm?
Solve the system of equations by the addition method. 0.01x-0.08y=-0.1 0.2x+0.6y=0.2
The domain of the function f(x)=x+7x2βˆ’144 is (βˆ’βˆž,), ( ,), and ( , ∞).