Question

A house is for sale for $250,000. You have a choice of two 20 year mortgages with monthly payments: 1) if you make a down payment of $25,000, you can obtain a loan at 6% interest, or 2) if you make a down payment of $50,000 you can obtain a loan at 5% interest. What is the effective annual rate of interest on the additional $25,000 borrowed with the first loan? I know the answer is 12.95% but i dont know how they got that.

Answer 1

Using calculator:
Step 1: Original Monthly Payment
N=12*20
PV=-225000
I/Y=6%/12
FV=0
CPT PMT=1611.96988157587

Step 2: New Monthly Payment
PV=-200000
I/Y=5%/12
N=12*20
FV=0
CPT PMT=1319.91147843331

Step 3: Rate on borrowed amount
FV=0
N=12*20
PV=-25000
PMT=1611.96988157587-1319.91147843331=292.058403142556
CPT I/Y=1.079%
Hence, return=1.079%*12=12.95%

ALTERNATIVELY Use the below formula in excel:
=RATE(20*12,PMT(6%/12,12*20,-225000)-PMT(5%/12,12*20,-200000),-25000,0)*12
=12.95%