Question

11. How many monthly payments remain to be paid on an 8% mortgage with a 30-year amortization and monthly payments of $733.76, when the balance reaches one-half of the $100,000 mortgage?

Please show how to retrieve answers with formula.

Answer 1

Amount of monthly payment ( A) = $733.76

Remaining balance of loan (P) = 100,000/2 = $50,000

APR = 8%

Monthly interest rate (i) = 8%/12 = 0.0066667

Remaining monthly payments = n

To find "n" we can use "(P/A,i,n)" i.e "to find P, given A" equation, as provided below,

P= A* l i (1+i)"

P = ī i(1+i)n

i(1+i)n

(1+n = 4-Pi

(1 + i)" = 4-Pi

taking log both side,

n * log(1+i) = log " LA- Pi -

n = log G-R) log(1+i)

putting the values,

log ( 733.76-50,000 0.0066667 log(1 +0.0066667) "

= log(1.832445392) Log(1.0066667)

n = 0.26303104 0.002885688

n = 91.15019348

n = 91.15

Thus, Remaining monthly payments is 91 months (rounded)

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.