Question

Assume Jimmy borrows $554,238.40 today for a house mortgage, and plans to pay back in full after paying for 20 years. If the interest rate is 10.2% and it will compound semiannually, how much should Jimmy pay each year?

Answer 1

Effective rate of interest = (1+r/n)^n -1
n= number of periods in a year
r = interest rate
= (1+0.102/2) ^2 - 1
=10.77563%
Annual payment   = [P x R x (1+R)^N]/[(1+R)^N-1]
Where,
P= Loan Amount
R= Interest rate per period
N= Number of periods
= [ $554238.4x0.1077563 x (1+0.1077563)^20]/[(1+0.1077563)^20 -1]
= [ $59722.67930192( 1.1077563 )^20] / [(1.1077563 )^20 -1
=$68580.25