Question

Darlene Ramirez bought a home for $140,000. She put 20% down with a mortgage rate of 7.5% for 25 years. Her yearly payments are:

Answer 1

so how much does she have to borrow if shes paid 20% upfront?

Answer 2

also its an odd statement, early payments.

most mortagages are a monthly payment, so would they want total payments made per year? or are we determining that a payment is made once a year?

Answer 3

**yearly payments is an odd statement ....

Answer 4

it is asking for the payment made once a year

Answer 5

ok ... thats doable

Answer 6

do you have a formula you use? or should we make one that I made up myself?

Answer 7

given a number of payment periods, n, for a given loan amount B, and a stated periodic compounding rate, k, the balance of the loan at any point in time is determined as:
\[B_n=Bk^n-P\frac{k^n-1}{k-1}\]
the loan is paid when Bn = 0, so we can solve for P, payments
\[0=Bk^n-P\frac{k^n-1}{k-1}\]
\[Bk^n=P\frac{k^n-1}{k-1}\]
\[P=Bk^n\frac{k-1}{k^n-1}\]
which we can reduce to the textbook formula but i find this version more useful

Answer 8

\[P=140000(1+.075)^{25}\frac{(1+.075)-1}{(1+.075)^{25}-1}\]

Answer 9

forgot to remove the 20% down payent of course but thats just an adjustment to B

Answer 10

we are borrowing 80% of 140 000 so multiply the results by .80

Answer 11

so we don't use the 20% down payment?

Answer 12

so we don't use the 20% down payment?

Answer 13

we did

we paid in 20% of 140000 so the amount needed to borrow is the remaining 80% of 140000

our original balance is therefore just 140000(.80)

Answer 14

we can either figure that number out, or just adjust the balance as is by multiplying it by .80

Answer 15

\[P=140000(\color{red}{.80})(1+.075)^{25}\frac{(1+.075)-1}{(1+.075)^{25}-1}\]