Question

A person agrees to pay $360,000 in 40 annual partial payments that form an arithmetic progression when 30 payments have been made, and then the person stops paying. Determine the value of the first payment, also what is the value the difference of the common arithmetic progression

70

likes
348 views

Answer to a math question A person agrees to pay $360,000 in 40 annual partial payments that form an arithmetic progression when 30 payments have been made, and then the person stops paying. Determine the value of the first payment, also what is the value the difference of the common arithmetic progression

Expert avatar
Cristian
4.7
116 Answers
1. La suma de 40 pagos parciales que forman una progresión aritmética es igual al monto total.
2. La fórmula de la suma de una progresión aritmética es:
S_n = \frac{n}{2} \left( 2a_1 + (n-1)d \right)
3. Dado que el total pagado es S_{40} = 360,000 y n = 40 , se tiene:
360,000 = \frac{40}{2} \left( 2a_1 + 39d \right)
360,000 = 20 \left( 2a_1 + 39d \right)
18,000 = 2a_1 + 39d
4. Cuando se ha realizado el pago de 30 cuotas:
S_{30} = \frac{30}{2} \left( 2a_1 + (30-1)d \right)
S_{30} = 15 \left( 2a_1 + 29d \right)
5. Suponemos que para 30 pagos, $ S_{30} $ también es proporción de $ S_{40} $:
\frac{30}{40} \cdot 360,000 = 270,000
270,000 = 15 \left( 2a_1 + 29d \right)
18,000 = 2a_1 + 29d
6. Tenemos dos ecuaciones:
18,000 = 2a_1 + 39d
18,000 = 2a_1 + 29d
7. Restando la segunda de la primera:
10d = 0
d = 150
8. Sustituyendo $ d $ de vuelta a una de las ecuaciones:
18,000 = 2a_1 + 29(150)
18,000 = 2a_1 + 4,350
13,650 = 2a_1
a_1 = 3,000
9. Por lo tanto, el primer pago es:
a_1 = 3,000
10. Y la diferencia común es:
d = 150

Frequently asked questions (FAQs)
What is the derivative of cos(3x^2 + 5) with respect to x?
+
What is the limit as x approaches infinity of (5x^2 - 3x + 2) / (2x^2 - x + 1)?
+
What is the sum of 68 and 97?
+
New questions in Mathematics
8x²-30x-10x²+70x=-30x+10x²-20x²
The patient is prescribed a course of 30 tablets. The tablets are prescribed “1 tablet twice a day”. How many days does a course of medication last?
How do you think the company has increased or decreased its income?
Consider numbers from 1 to 2023. We delete 3 consecutive numbers so, that the avarage of the left numbers is a whole number
(5u + 6)-(3u+2)=
A regional candy factory sells a guava roll at a price of $48, the monthly fixed costs amount to $125,000 and the variable cost for making a guava roll is $28. Determine: a) The equation of the total income from the production of guava rolls.
A company that manufactures personal hygiene items purchases machinery for $220,000 that is considered to last 7 years; it is estimated that at the end of the period it will have a salvage value of $1000. Find: to. The depreciation rate. b. The book value at the end of the sixth year.
A person borrows rm 1000 from a bank at an interest rate of 10%. After some time, he pays the bank rm 1900 as full and final settlement of the loan. Estimate the duration of his loan.
15/5+7-5
Raúl, Gilberto and Arturo are playing golf; The probabilities of winning for each one are as follows: (Raúl wins) = 20% (Gilberto wins) = 0.05% (Arturo wins) = ¾%. Perform operations and order events from least to most probable.
The price per night of a suite at the Baglioni Hotel in Venice is 1896 euros, VAT included. The VAT in Italy is 25%. The hotel gets a return of 10% out of the price VAT included. a) What is the amount of VAT paid by the hotel for one
Given (3x+2)E [2;14] how much money (in soles) does Sophia have if numerically it is the greatest value of x?
I. Order to add 40.25+1.31+.45 what is the first action to do ?
3/9*4/8=
Use linear approximation to estimate the value of the sine of 31o.
-1%2F2x-4%3D18
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
We have two distributions: A (M = 66.7, 95% CI = [60.3, 67.1]) / B (M = 71.3 95% CI = [67.7, 74.9]). Erin maintains that B is significantly larger than A. Provide your opinion on Erin’s argument and justify your opinion.
Consider the function f(x)=1/2(x+1)^2-3. Use the preceding/following interval method to estimate the instantaneous rate of change at 𝑥 = 1.
Question 3 A square has a perimeter given by the algebraic expression 24x – 16. Write the algebraic expression that represents one of its sides.