Does anyone know this hard math question?

Question

PV=R[1-(1+i)negative n]
_____________________
i


where PV = 14 828.43
R = 325
i = .025 divided by 12
n = 48

the answer is 15 973.00

i have asked many people this question to show me how to get the answer but they don't know how.(i even asked the teacher and the teacher didn't know)

i was wondering if someone could find out how it is done (the answer is given) or if there is some website that has a calculator that can give me the steps on how to get the answer.

Answer 1

When I run the numbers given, I get
PV = 14,830.68
or
R = 324.95

Given PV = 15,973.00, the easiest value to solve for is R, so R = 350.03

PV=R[1 - (1 + i)^-n]/i is the formula for finding the initial, or present value (PV) of a mortgage with fixed payments (R) and monthly interest (i) compounded monthly (n)

Solving for R, you have
R = i*PV/[1 - (1 + i)^-n],
which gives you the payments necessary to pay off a loan at the given interest rate and number of months.

The equation can also be solved for n, but a solution for i becomes transcendental and has to be iterated.

The easiest keystroke sequence for calculating
PV=R[1 - (1 + i)^-n]/i is:

0.025 [ / ] 12 [ = ] MS [ + ] 1 [ = ] [x^y] 48 [+/-] = [+/-] + 1 [ = ] [ * ] 325 [ / ] MR [ = ]

"What if" solutions are better done on a spreadsheet, where you only have to enter the formula once, and can then change any of the independent variables to get the change in the solution.

Answer 2

PV=R[1-(1+i)negative n]
_____________________
i
where PV = 14 828.43
R = 325
i = .025 divided by 12
n = 48
PV= {R[1-(1+i)negative n]}/i
i= .025/12 = 0.0020833
The negative n is confusing. Did you mean exponent n? Otherwise why not just say -n? This looks like an interest problem where 14,828.43 is compounded monthly at a rate of 2.5% per year for 4 years (48 months).

The correct formula is P = PV(1+r/12)^48
where PV is amount you started with
r is the interest rate per year

PV = 14,828.43(1+ .025/12)^48
PV= 14,828.43(1.0020833)^48
PV= 14,828.43(1.1050542)
PV= 16, 386.21

This is not the same as your answer.

Your R = 325 does not make sense to me, just as your negative n is confusing. I suggest you look at the problem again and state the problem more clearly. As it is your equation leaves nothing to be solved since you have supplied all the parameters. If we were to plug in the values you have given into the equation, we would find that we had an inequality, not an equation.

Answer 3

The formula you have there is for annuities. It says that, if you borrow an amount PV and pay it off with n payments at a monthly interest rate of i, your monthly payment is R. You have specified a correct set of values, that is, if you borrow $14828.43 at 2.5% per year and pay it back in monthly payments of $325 it will take 4 years (48 payments) to pay off the loan.

You state the answer is 15973. This must be a present value (PV) or a future value (FV). The future value is: FV = PV(1 + i)^n. For your given values, the FV 16386.23.

In order to get the PV to match you must alter the payment, interest, or period of the loan.

A payment of 350 per month corresponds to your PV of 15973. SInce this is a nice round number, I am guessing that the problem statement might have been to calculate the loan amount for a $350 per month payment.

Answer 4

a million+a million=2 besides, somebody with some distance too lots time on their palms desperate to instruct it... "The information starts from the Peano Postulates, which define the organic numbers N. N is the smallest set fulfilling those postulates: P1. a million is in N. P2. If x is in N, then its "successor" x' is in N. P3. there is not any x such that x' = a million. P4. If x isn't a million, then there's a y in N such that y' = x. P5. If S is a subset of N, a million is in S, and the implication (x in S => x' in S) holds, then S = N. then you certainly could define addition recursively: Def: permit a and b be in N. If b = a million, then define a + b = a' (utilising P1 and P2). If b isn't a million, then permit c' = b, with c in N (utilising P4), and define a + b = (a + c)'. then you certainly could define 2: Def: 2 = a million' 2 is in N via P1, P2, and the definition of two. Theorem: a million + a million = 2 information: Use the 1st area of the definition of + with a = b = a million. Then a million + a million = a million' = 2 Q.E.D. notice: there is yet another formula of the Peano Postulates which replaces a million with 0 in P1, P3, P4, and P5. then you certainly could replace the definition of addition to this: Def: permit a and b be in N. If b = 0, then define a + b = a. If b isn't 0, then permit c' = b, with c in N, and define a + b = (a + c)'. you besides could could define a million = 0', and a couple of = a million'. Then the information of the thought above is a splash distinctive: information: Use the 2nd area of the definition of + first: a million + a million = (a million + 0)' Now use the 1st area of the definition of + on the sum in parentheses: a million + a million = (a million)' = a million' = 2 Q.E.D." Wow, he could be a real hit with the girls...!! :)

Answer 5

Does anyone know this hard math question?
PV=R[1-(1+i)negative n]

You have give the number values of the unknown. What are you asking for.
Does the negative n mean multiply by minus n ?
Do you divide the right hand side of the equation by i ?
Usually you have an unknown and you want to calculate it.
In your case it's not clear what you are asking for.
If you update your information I might be able to help you.

Brenmore.

Answer 6

This looks like a present value calculation.

I'll answer your question by talking about compound interest.

Let's say you have a sum of money S.

You have it invested in savings for interest rate i.

So after one year you have Future money F, = S(1+i)

After another year, you get interest, and it compounds, earning interest on the interest.

So, for N years, compounded annually, you get:

F = S * (1+i)^n

Now, you could compound the interest more often annually. Say you did this K times a year. K could be twelve, or monthly.

Then:

F = S * ( 1 + i/K)^n*k

So, we are saying that the fraction (1+i/K) is raised to the power of n times k.

Now, let's reverse the equation. Assuming an interest rate of i, how much is needed now to have F in the future.

S = F/(1 +i/k)^nk

Which can be changed to:

S = F* (1 + i/K) ^ (-nk)

which looks like your present value calculation.

Answer 7

It'd help if you write it in a clearer way: do you mean PV=(R[1-(1+i)(-n)] over i)? and what is the variable that equals 15973 (the question)?
Note: are you sure i=0.025/12? i is a math symbol that means sqrt(-1)

Answer 8

If you have the values for all the variables, what are you actually solving?
And if the two sides of the "equation" are not equal then by definition there is no solution.

Answer 9

fill in all the numbers and use ytour calculator

325* (1-(1+(0.025/12))-48)

that is allthe answer you are giving is clearly wrong way to big

Answer 10

What is the question? You have stated all the possible variables and therefore there is no question....