Question

Beth is taking out a loan to purchase a new home. She is financing $50,000 for 25 years at an interest rate of 14.25%. What is her monthly payment?

A- $158.68

B - $220,140

C - $138.89

D - $611.50
There's also a table that goes with it that says the term for the rate of 14.25% is 12.23.

Answer 1

The present value (PV) of a loan for n years at r% compounded t times a year where there is equal P periodic payments is given by:


`PV=P\left( (1-\left(1+ (r)/(t) \left)^(-nt))/( (r)/(t) ) \right)`

Given that Beth is taking out a loan of PV = $50,000 to purchase a new home for n = 25 years at an interest rate of r = 14.25%. Since she is making the payment monthly, t = 12.

Her monthly payment is given by:


`50,000=P\left( (1-\left(1+ (0.1425)/(12) \right)^(-25*12))/( (0.1425)/(12) ) \right) \\ \\ =P\left( (1-(1+0.011875)^(-300))/( 0.011875 ) \right)=P\left( (1-(1.011875)^(-300))/( 0.011875 ) \right) \\ \\ =P\left( (1-0.028969)/( 0.011875 ) \right)=P\left( (0.971031)/( 0.011875 ) \right)=81.770994P \\ \\ \therefore P= (50,000)/(81.770994) =\$611.46`

Therefore, her monthly payment is about $611.50