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Homework answers / question archive / A house is for sale for $250,000

A house is for sale for $250,000

Finance

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%

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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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