Maximum Affordable Mortgage Calculation

[physicsgal]

Homework Statement

alice wants to take out a 20 yr mortage. the interest rate is 8% compounded semi-annually. alice can afford monthly payments of $850. what is the largest mortage that she can afford?

Homework Equations

The Attempt at a Solution

this is using a graphing calculator:
N= 20 x 12 = 240
I%= 8
*PV= 102 612.70?
PMT= -850
FV = 0
P/Y = 12
C/Y = 2
PMT = END

but I am suppose to solve this without a graphing calculator.

PV = (R(1-(1/1+i)^n)/i

R = 850
n = 240
i = ?
for i i had 1.04^(1/8) - 1 = 0.004914626.. i think that's where my problem is. but dunno.

for the answer i got $119,628.45... but that doesn't match the $102,612.70 from my graphing calculator.

any help is appreciated

~Amy

 

[HallsofIvy]

Homework Statement

alice wants to take out a 20 yr mortage. the interest rate is 8% compounded semi-annually. alice can afford monthly payments of $850. what is the largest mortage that she can afford?

Homework Equations

The Attempt at a Solution

this is using a graphing calculator:
N= 20 x 12 = 240

This, immediately, is wrong. N is the number of "compounding intervals". If this is "compounded semi-annually" for 20 years, how many times is it compounded?

I%= 8
*PV= 102 612.70?
PMT= -850
FV = 0
P/Y = 12
C/Y = 2
PMT = END

but I am suppose to solve this without a graphing calculator.

PV = (R(1-(1/1+i)^n)/i

R = 850
n = 240
i = ?

8% of course: 0.08 so 1+ i= 1.08.

for i i had 1.04^(1/8) - 1 = 0.004914626.. i think that's where my problem is. but dunno.

for the answer i got $119,628.45... but that doesn't match the $102,612.70 from my graphing calculator.

any help is appreciated

~Amy

 

[Gib Z]

Now since its compounded 2 times a year for 20 years its compounded 40 times.
Since we've fixed your expression for total she can pay, which is 204,000, set them equal and solve for the original value.

 

[physicsgal]

thanks for the help. but it turns out that instead of 1.04^(1/8) - 1 = 0.004914626.. it should have been 1.04^(1/6) -1 =0.006558197.. that gives me $102,612.70 (same answer as i got with the graphing calculator).

~Amy