Question

16. John is buying a house for $1,000,000. He can get a 30-year loan on 80% of the purchase price at 7.25% with monthly payments, or he can get a 15-year monthly payment loan at 6.5% with the 20% downpayment.

a. What would his payments be for each loan? [$5457.41; $6968.86]

b. How much interest is paid over the life of each loan? [$1,164,667.60; $454,394.80]

Answer 1

Question a:

PV = Loan Amount = $1,000,000 * 80% = $800,000

n1 = 30*12 = 360 months

r1 = monthly interest rate = 7.25%/12 = 0.6041666667%

n2 = 15*12 = 180 months

r2 = monthly interest rate = 6.5%/12 = 0.5416666667%

Monthly loan payment for 30 year loan = [r*PV] / [1 - (1+r)^-n]

= [0.6041666667% * $800,000] / [1 - (1+0.6041666667%)^-360]

= $4,833.33333333 / 0.88564596033

= $ 5457.41024046

= $5,457.41

Monthly loan payment for 15 year loan = [r*PV] / [1 - (1+r)^-n]

= [0.5416666667% * $800,000] / [1 - (1+0.5416666667%)^-180]

= $4,333.33333333 / 0.62181389831

= $ 6968.85892243

= $6,968.86

Monthly payments for 30 year loan is $5,457.41

Monthly payments for 15year loan is $6,968.86

Question b:

Interest paid over life of 30 year loan = [360 * $5,457.41] - $800,000

= $1,964,667.6 - $800,000

= $1,164,667.6

Interest paid over life of 15 year loan = [180 * $6,968.86] - $800,000

= $1,254,394.8 - $800,000

= $454,394.8

Interest paid over life of 30 year loan is $1,164,667.6

Interest paid over life of 15year loan is $454,394.8