You plan to take out a $300,000 conventional fixed rate mortgage. You will eithe

Question

You plan to take out a $300,000 conventional fixed rate mortgage. You will either take out a 15 year mortgage or a 30 year mortgage. The interest rate on the 15 year mortgage is 3.5%. The interest on the 30 year mortgage is 4.5%. What will be the monthly mortgage payment for the 15 year mortgage? What will be the monthly mortgage payment for the 30 year mortgage?

$3,042.80 and $4,294.02

$3,059.68 and $4,341.25

$1,539.49 and $2,170.63

$1,520.06 and $2,144.65

$3,042.80 and $4,294.02

$3,059.68 and $4,341.25

$1,539.49 and $2,170.63

$1,520.06 and $2,144.65

Explanation / Answer

let x be the monthly payment

PV of monthly payments = loan amount = 300,000

PV of monthly payments = x * [1-(1+i)^n]/i

i = interest rate per period

n = number of periods

for 15 year mortage

i = 3.5%/12

number of periods = 15 * 12 = 180

=>

300000 = x * [1-(1+3.5%/12)^-180]/(3.5%/12)]

x = 2144.65

for 30 year mortage

i = 4.5%/12

number of periods = 30 * 12 = 360

=>

300000 = x * [1-(1+4.5%/12)^-360]/(4.5%/12)]

x = 1520.06

hence the answer is

d.  
$1,520.06 and $2,144.65

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