Question

"You decide to purchase a building for $30,000 by paying $5,000 down and assuming a mortgage of $25,000. The bank offers you a 15-year mortgage requiring annual end-of-year payments of $3,188 each. The bank also requires you to pay a 3 percent loan origination fee, which will reduce the effective amount the bank lends to you. Compute the annual percentage rate of interest of this loan."

Answer 1

10%

Step-by-step explanation:

total loan = $25,000 x (1 - 3%) = $24,250

the present value of an annuity formula:

PV = annual payment x annuity factor

annuity factor = PV / annual payment = $24,250 / $3,188 = 7.607

the formula to calculate PV annuity factor is [1 - 1/(1 + i)ⁿ ] / i

7.607 = [1 - 1/(1 + i)¹⁵ ] / i

7.607i = 1 - 1/(1 + i)¹⁵

1/(1 + i)¹⁵ = 1 - 7.607i

1 / (1 - 7.607i) = (1 + i)¹⁵

after a lot of math:

i = 10%

1 / (1 - 0.7607) = 1.1¹⁵

4.18 = 4.18