Calculating monthly payments on a mortgage

J

Jill

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Mar 4, 2009
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Here we go again:

Ricky and Lucy have decided to refinance their home mortgage loan. Their current home mortgage loan is for $500,000. The mortgage interest rate is 6.75% and it is to be paid off in 30 years with equal monthly payments. After 3 full years of payments, Ricky and Lucy will refinance the balance at 3.0%, to be paid off in 15 years with equal monthly payments. What will Ricky and Lucy's new monthly payments be? (Please be sure to show how calculations are made. Excel alone is not sufficient. Be careful with round-off, because a mortgage payment includes cents, as well. Answer must be precise.

I guess I will have to first find the monthly payment and then the new monthly paments.

Find the monthly payments of 500K @ 6.75% at 30 Yrs.
FV=500K
N=30
i= 6.75 or .0675
so would it be:

P[i(1+i)^n]/[(1+i)^n-1

Monthly payment i=i/12
500K compounded @ .0675 for 30yrs solve for i:

i=.0675/12=.005625
and n as 12X30 = 360 monthly payments

solve for :
(1+i)^n = (1.0056250^360 = 7.533245477

M = P[i (7.533245477)]/[7.533245477-1]
M= [(.005625) X (7.533245477]/6.533245477
= 500,000(.006485981)
= 3242.9905
Monthly payment =$3,243

If this is correct that's as far as I can get.

If my answer is correct so far I need to figure out what that montly payment is for the full 3years then use that payment amount and find out what it will be in 15 years discounted at 3.0%.

I don't know how to proceed from here please show me the calculations???
Please help!!
 
Your payment calculation of 3242.9905 is CORRECT: yer doin' great!

Step#1: calculate balance owing after 3 years, which means after 36 payments of 3242.9905.
To do that, calculate the FV of 500000 and the FV of 36 payments of 3242.9905;
subtract them and that'll be the mortgage balance after 36 months; still with me?

Step#2: calculate the monthly payment on that balance owing, similarly to how you calculated the 3242.9905.

I'll let you have the pleasure of working that out :wink:
 
Eureka I think I got it :D :D !!!
After 3 years Ricky and Lucy paid: $3242.9905 X 36 = $116,747.658
? Find the balance on the mortgage after making 36 monthly payment:
P=500K
i= .005625
n = 36 months
M= 3242.9905
FV = P * (1+i) ^n – M * [(1+i) ^n-1/ (i)]
FV= 500000 * (1.005625) ^36 - (3242.9905) * [(1.005625) ^36 – 1/ (.005625)]
FV= 500000* (1.223765518) – (3242.9905) * [(1.223765518) -1)/ (.005625)]
FV= 611882.759 – (3242.9905) * (39.78053654)
= 611882.759 – 129007.9021
= 482874.8569
FV = $482,874.86
The remaining balance for the new loan will be $482,874.86
Part B. Find the new refinance monthly payment:
P [i (1+i) ^n]/ [(1+i) ^n-1
Monthly payment i=i/12
$482,874.86 @ .03 for 15yrs solve for i:
i=.03/12=.0025
And n as 12 X 15 = 180 monthly payments
Solve for: (1+i) ^n = (1.0025) ^180 = 1.567431725
i=.0025
n= 180
P = 482,874.86
M =?
M = P [i (1.567431725)]/ [(1.567431725)-1]
M= (482,874.86)* [(.0025) X (1.567431725)]/ (.5674317247)
M= (482,874.86) * (.0039185793)/(.5674317247)
M= (482,874.86) (.069058164)
M = $3,334.645129
Monthly payment =$3,334.65
After refinancing, Rick and Lucy will be paying a monthly payment of $3,334.65.
 
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