Question

An firm borrowed $203,000 to remodel their office. The load was to be paid back in equal monthly payments over 30 years at 5% interest, compounded monthly. After 12 years, the firm wants to pay off the loan. What is the remaining balance that must be paid off? Express your answer in $ to the nearest $1,000.

Answer 1

i = 5% / 12 = 0.4167% per month

t = 30 * 12 = 360 months

Monthly loan payment = 203000 * (A/P, 0.4167%,360)

= 203000 * 0.004167 * ((1 + 0.004167)^360)/((1 + 0.004167)^360-1)

= 203000 * 0.004167 * ((1.004167)^360)/((1.004167)^360-1)

= 203000 * 0.00536846

= 1089.80

No. of payments left after 12 yrs = 12 * (30 - 12) = 12 *18 = 216

Principal due after 12 yrs = 1089.80 * (P/A, 0.4167%,216)

= 1089.80 * ((1 + 0.004167)^216-1)/(0.004167 * (1 + 0.004167)^216)

= 1089.80 * ((1.004167)^216-1)/(0.004167 * (1.004167)^216)

= 1089.80 * 142.236292

= 155008.76 ~ 155000 (Rounded to nearest 1000)