Question

You decide to buy a condo after graduation and will borrow $100,000. If you take out a loan with a 5.75% APR and expect to pay it back monthly over 20 years. How much of the first monthly payment is principle?

Please answer using two decimal places and do not put the $ in your answer.  

Answer 1

Loan Amount = PV = $100,000

n = 20*12 = 240 months

r = monthly interest rate = 5.75%/12 = 0.47916667%

Monthly loan payment = [r*PV] / [1 - (1+r)^-n]

= [0.47916667% * $100,000] / [1 - (1+0.47916667%)^-240]

= $479.16667 / 0.682492665

= $702.083251

Monthly loan payment is $702.08

Interest on loan for the first month = $100,000 * 0.47916667% = $479.17

Principal amount on first month loan payment = Monthly lon payment - Interest on loan for the first month

= $702.08 - $479.17

= $222.91

Therefore, principal amount on first month loan payment is $222.91