An 800000 balloon mortgage has terms of 305 with a 5 interes

An $800,000 balloon mortgage has terms of 30/5 with a 5% interest rate. What is the monthly payment rounded to the nearest dollar?

a. $2,222

b. $2,333

c. $4,295

d. $4,677

Solution

The given $800000 balloon mortgage is amortized over 30 years , has balloon payment due in 5 years, and has a fixed interest rate of 5%.

The formula used to calculate the fixed monthly payment (P) required to fully amortize a loan of $ L over a term of n months at a monthly interest rate of r is

P = L[r(1+ r)ⁿ]/[(1 + r)ⁿ - 1]. Here, L = $800000, r = (5/100)*1/12 =5/1200= 1/240 and n = 30*12 = 360 so that P = 800000[ 1/240 ( 1+1/240)³⁶⁰]/[( 1+1/240)³⁶⁰-1] = [(800000/240)(241/240)³⁶⁰]/[(241/240)³⁶⁰-1] = (10000/3)*4.467744319/3.467744319 = $ 4294.57 or, $ 4295 ( on rounding off to the nearest Dollar). Option ( c ) is the correct answer