Question

You decide to buy a condo 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?

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