Find the monthly payment and estimate the remaining balance. Assume interest is

Question

Find the monthly payment and estimate the remaining balance. Assume interest is on the unpaid balance.
Thirty year mortgage for $310,000 at 4.14%: remaining balance after 12 years.
Specifically what I am looking for is how to solve for the second half of the problem. Everything in the beginning makes sense. I get that the monthly payment on the mortgage is $1505.12, but when I have to solve for the remaining balance I cannot figure it out. My friend told me that you solve for X and that X=144 in this problem. How do you find X!? Find the monthly payment and estimate the remaining balance. Assume interest is on the unpaid balance.
Thirty year mortgage for $310,000 at 4.14%: remaining balance after 12 years.
Specifically what I am looking for is how to solve for the second half of the problem. Everything in the beginning makes sense. I get that the monthly payment on the mortgage is $1505.12, but when I have to solve for the remaining balance I cannot figure it out. My friend told me that you solve for X and that X=144 in this problem. How do you find X!?
Thirty year mortgage for $310,000 at 4.14%: remaining balance after 12 years.
Specifically what I am looking for is how to solve for the second half of the problem. Everything in the beginning makes sense. I get that the monthly payment on the mortgage is $1505.12, but when I have to solve for the remaining balance I cannot figure it out. My friend told me that you solve for X and that X=144 in this problem. How do you find X!?

Explanation / Answer

EMI = [P x R x (1+R)^N]/[(1+R)^N-1], where P stands for the loan amount or principal, R is the interest rate per month [if the interest rate per annum is 11%, then the rate of interest will be 11/(12 x 100)], and N is the number of monthly instalments

EMI= (310000 * 0.0414/12 * (1+0.0414)^(30*12))/((1+0.0414/12)^(30*12) - 1) = $1,505.12

Remaining balance after 12years can be found out by finding total present value of EMI to be paid during remaining tenure i.e. (30-12 = 18 years at the end of 12 years.

P0=1505.12(1-(1+0.0414/12)^(-18*12))/(0.0414/12) = $228,913.59

Remaining balance after 12 years = $228,913.59

Here X=144, as advised by friend is number of payments made (12*12 = 144)

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