On January 1,2011,Zenith,Inc.signed a $200,000,5%,20-year mortgage note to buy a new office building.The mortgage will be repaid in a series of twenty equal annual installment payments.Calculate the amount of each payment.Round your answer to the nearest dollar.
A)$10,000
B)$16,049
C)$10,500
D)$20,000

Question

Quizplus · Accepted Answer

We can use the formula for the present value of an annuity to calculate the amount of each payment:
PV = PMT * [1 - (1+r)^(-n)] / r
Where PV is the present value of the mortgage (which is the amount borrowed), PMT is the amount of each payment, r is the interest rate per period (which is 5%/20 = 0.25%), and n is the total number of periods (which is 20).

Plugging in the values, we get:
200,000 = PMT * [1 - (1+0.0025)^(-20)] / 0.0025

Solving for PMT, we get:
PMT = 16,048.53

Rounding to the nearest dollar, the answer is:
B) $16,049