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Quick mortgage math question

164
0
1. 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?


2. Homework Equations



3. 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 im 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 doesnt match the $102,612.70 from my graphing calculator.

any help is appreciated

~Amy
 

HallsofIvy

Science Advisor
Homework Helper
41,728
881
1. 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?


2. Homework Equations



3. 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 im 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 doesnt match the $102,612.70 from my graphing calculator.

any help is appreciated

~Amy
 

Gib Z

Homework Helper
3,344
4
Now since its compounded 2 times a year for 20 years its compounded 40 times.
Since weve fixed your expression for total she can pay, which is 204,000, set them equal and solve for the original value.
 
164
0
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
 

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