Question

A loan is repaid with payments of $2226 made at the end of each month for 12 years. If interest on the loan is 5.2%, compounded semi-annually, what is the initial value of the loan? Enter to the nearest cent (two decimals). Do not use $ signs or commas.

219

likes
1096 views

Answer to a math question A loan is repaid with payments of $2226 made at the end of each month for 12 years. If interest on the loan is 5.2%, compounded semi-annually, what is the initial value of the loan? Enter to the nearest cent (two decimals). Do not use $ signs or commas.

Expert avatar
Murray
4.5
92 Answers
To find the initial value of the loan, we can use the formula for the present value of an ordinary annuity:

PV = \frac{P}{r} \left(1 - \frac{1}{(1+r)^n}\right)

where:
- PV is the present value or initial value of the loan
- P is the payment amount made at the end of each period (monthly)
- r is the interest rate per period (semi-annually)
- n is the total number of periods (monthly payments for 12 years = 12 * 12 = 144 periods)

First, let's convert the interest rate from annual to semi-annually:

r = \frac{5.2}{2} = 2.6\% = 0.026

Now we can calculate the initial value of the loan using the given values:

PV = \frac{2226}{0.026} \left(1 - \frac{1}{(1+0.026)^{144}}\right)

Simplifying the equation:

PV = \frac{2226}{0.026} \left(1 - \frac{1}{(1.026)^{144}}\right)

Calculating the present value:

PV=\frac{2226}{0.026}\left(1-\frac{1}{(1.026)^{144}}\right)\approx83.475

Therefore, the initial value of the loan is approximately 83.475

Frequently asked questions (FAQs)
Math Question: Evaluate the limit of f(x) = (e^x - 1 - x) / (sin(x) - x) as x approaches 0.
+
Question: Solve for x: 3x + 2 = 17.
+
What is the derivative of sin(x)cos(x) + ln(x^2 + 3x) - e^x + sqrt(2x^3) with respect to x?
+
New questions in Mathematics
a runner wants to build endurance by running 9 mph for 20 min. How far will the runner travel in that time period?
5 . {2/5 + [ (8/-9) - (1/-7) + (-2/5) ] ÷ (2/-5)} . 8/15
11(4x-9)= -319
Solve: −3(−2x+23)+12=6(−4x+9)+9.
Kayla has $8,836.00 in her savings account. The bank gives Kayla 5%of the amount of money in account as a customer bonus. What amount of money does the bank give Kayla? Justify your answer on a 6th grade level.
How many kilometers does a person travel in 45 minutes if they move at a rate of 8.3 m/s?
132133333-33
Find the measures of the sides of ∆KPL and classify each triangle by its sides k (-2,-6), p (-4,0), l (3,-1)
Moaz wanted to test whether the level of headache pain (on a scale of 1 – 10) changes after taking Advil. He collected data from 9 participants and calculated the difference in headache pain before and after taking Advil (summarized in the table below). Determine W observed for this test. Difference Scores -2 -4 0 +1 +3 -2 0 -3 -5 Also, What is the degrees of freedom for this test?
Divide 22 by 5 solve it by array and an area model
Estimate the fifth term if the first term is 8 and the common ratio is -1/2
How many different ways can a psychology student select 5 subjects from a pool of 20 subjects and assign each one to a different experiment?
We have spent 1/4 of the inheritance on taxes and 3/5 of the rest on buying a house. If the inheritance was a total of €150,000 How much money do we have left?
3. A rock is dropped from a height of 16 ft. It is determined that its height (in feet) above ground t seconds later (for 0≤t≤3) is given by s(t)=-2t2 + 16. Find the average velocity of the rock over [0.2,0.21] time interval.
With the aim of identifying the presence of the feline leukemia virus (FeLV), blood samples were collected from cats sent to a private veterinary clinic in the city of Belo Horizonte. Among the animals treated, it was possible to observe that age followed a Normal distribution with a mean of 4.44 years and a standard deviation of 1.09 years. Considering this information, determine the value of the third quartile of the ages of the animals treated at this veterinary clinic. ATTENTION: Provide the answer to exactly FOUR decimal places
User One of the applications of the derivative of a function is its use in Physics, where a function that at every instant t associates the number s(t), this function s is called the clockwise function of the movement. By deriving the time function we obtain the velocity function at time t, denoted by v(t). A body has a time function that determines its position in meters at time t as S(t)=t.³√t+2.t . Present the speed of this body at time t = 8 s.
Let v be the set of all ordered pairs of real numbers and consider the scalar addition and multiplication operations defined by: u+v=(x,y)+(s,t)=(x+s+1,y+t -two) au=a.(x,y)=(ax+a-1,ay-2a+2) It is known that this set with the operations defined above is a vector space. A) calculate u+v is au for u=(-2,3),v=(1,-2) and a=2 B) show that (0,0) #0 Suggestion find a vector W such that u+w=u C) who is the vector -u D) show that axiom A4 holds:-u+u=0
How to factorise 5y^2 -7y -52
nI Exercises 65-68, the latitudes of a pair of cities are given. Assume that one city si directly south of the other and that the earth is a perfect sphere of radius 4000 miles. Use the arc length formula in terms of degrees to find the distance between the two cities. 65. The North Pole: latitude 90° north Springfield, Illinois: latitude 40° north
if y=1/w^2 yw=2-x; find dy/dx