A 30-year mortgage for $95,000 is issued at a 9% nominal interest rate. a. What

Question

A 30-year mortgage for $95,000 is issued at a 9% nominal interest rate.

a. What is the monthly payment

b. How long does it take to pay off the mortgage if $1,000 is paid?

c. How long does it take to pay off the mortgage, if double payments are made?

I think I got the interests already:

r 0.09 nominal interest rate
n 30 years
m 12 periods per year
i 0.008 monthly fixed
ia 0.094 yearly fixed
ia 0.008 monthly fixed
$764.391 Monthly Payment
$3,548.075 Yearly Payment

But I'm stuck on where to go from here. Thanks!

Explanation / Answer

n=30-year mortgage for PV=$95,000 is issued at a i=9% nominal interest rate. a. What is the monthly payment Monthly rate = 9%/12, nper = no of loan payments = 30 yrs * 12 month/yr = 360 months Using Excel PMT function, which is Monthly Payment =PMT(monthly rate, no of periods, PV) ie Monthly Payment = PMT(9%/12,360,-95000) = $764.39 b. How long does it take to pay off the mortgage if $1,000 is paid? If PMT = 1000, PV = -95000, Monthly Int rate i = 9%/12, what is nper? using nper excel function, we have No of Months = nper(monthly rate, PMT, PV) Ie No of months = nper(9%/12,1000,-95000) = 166.83 months ie 167 months So if we pay $1000 per month, the Loan wil be repaid in 167 months c. How long does it take to pay off the mortgage, if double payments are made? (1) Here we are assuming that double payment is 2*764.39 = 1528.78 If PMT = 1528.78, PV = -95000, Monthly Int rate i = 9%/12, what is nper? using nper excel function, we have No of Months = nper(monthly rate, PMT, PV) Ie No of months = nper(9%/12,1528.78,-95000) = 83.98 months ie 84 months So if we pay $1528.78 per month, the Loan wil be repaid in 84 months (2) Here we are assuming that double payment is 2*1000 = 2000 If PMT = 2000, PV = -95000, Monthly Int rate i = 9%/12, what is nper? using nper excel function, we have No of Months = nper(monthly rate, PMT, PV) Ie No of months = nper(9%/12,2000,-95000) = 58.95 months ie 59 months So if we pay $2000 per month, the Loan wil be repaid in 59 months

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