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A house is for sale for $250,000
A house is for sale for $250,000. You have a choice of two 20-year mortgage loans with monthly payments: (1) if you make a down payment of $25,000, you can obtain a loan with a 6% rate of interest or (2) if you make a down payment of $50,000, you can obtain a loan with a 5% rate of interest. What is the effective annual rate of interest on the additional $25,000 borrowed on the first loan?
a) 15.36%
b) 12.95%
c) 14.21%
d) 18.67%
Expert Solution
1) We can calculate the monthly payment by using the following formula in excel:-
=pmt(rate,nper,-pv,fv)
Here,
Pmt = Monthly payment
Rate = 6%/12 = 0.5% (monthly)
Nper = 20*12 = 240 periods (monthly)
PV = $250,000 - $25,000 = $225,000
FV = $0
Substituting the values in formula:-
=pmt(0.5%,240,-225000,0)
= $1,611.97
2) We can calculate the monthly payment by using the following formula in excel:-
=pmt(rate,nper,-pv,fv)
Here,
Pmt = Monthly payment
Rate = 5%/12 = 0.4167% (monthly)
Nper = 20*12 = 240 periods (monthly)
PV = $250,000 - $50,000 = $200,000
FV = $0
Substituting the values in formula:-
=pmt(0.4167%,240,-200000,0)
= $1,319.91
We can calculate the effective interest rate by using the following formula in excel:-
=rate(nper,pmt,-pv,fv)
Here,
Rate = Effective interest rate (monthly)
Nper = 20*12 = 240 periods (monthly)
Pmt = $1,611.97 - $1,319.91 = $292.06
PV = $25,000
FV = $0
Substituting the values in formula:-
=rate(240,292.06,-25000,0)
= 1.08%
Effective annual rate of interest = 1.08% * 12
= 12.95%
Hence, the correct option is b) 12.95%
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