Question

The Ricordi family has just bought a house for $275,000. They have been saving money for a while and are able to make a $100,000 down payment. They have chosen a 30-year mortgage from their bank to borrow the balance of the purchase price. The interest rate of the mortgage is 6.5%, compounded monthly.

e) [4 pts] After ten years of payments, how much of their next monthly payment is devoted to interest?

Answer 1

10yrs of payment would mean 10yrs *12 months = 120 therefore after 120 months of payment it will be the 121st payment

For the 121st payment, you can use IPMT function in excel to arrive the interest portion

IPMT(rate, per,nper,PV,FV,Type)

rate 6.5%/12, per 121 (121st payment) nper 360 (Number of total payments are 360) PV 175000

IPMT(6.5%/12,121,360,175000)

$803.61 of the 121st monthly payment is devoted to interest

2nd Method (Manual)

House Cost $275000 less: down payment $100000 = Loan or present value $175000

Monthly rate or r 6.5% / 12 = 0.005416667

Total n or nper 30yrs * 12months = 360

PMT or Monthly payment formula = Present Value / [ 1- ( 1+r)^-n]/ r

Monthly payment = 200000 / ((1 - (1.005416667)^-360) / 0.005416667)

Monthly payment = 200000 / ((1 - 0.143024728) / 0.005416667)

Monthly payment = 200000 / (0.856975272 / 0.005416667)

Monthly payment = 200000 / 158.2108195

Monthly payment = 1106.12

You can make an amortization table using the concept mentioned below and manually check the interest portion for 121st payment

Month 1

The first interest payment will be (rate) * (beginning principal)

0.005416667 * 175000 =947.92

payment towards principal = Monthly Payment - interest portion

payment towards principal = 1106.12 - 947.92

payment towards principal = 158.20

Ending balance of principal = Beginning Principal Balance - payment towards Principal for that month

Ending balance of principal = 175000 - 158.20 = 174841.80

Month 2

Interest portion = (rate) * (ending principal)

0.005416667 * 174841.80 (ending principal) = 947.06

payment towards principal = Monthly Payment - interest portion

payment towards principal = 1106.12 - 947.06

payment towards principal = 159.06

Ending balance of principal = Principal Balance - payment towards Principal for that month

Ending balance of principal 174841.80 - 159.06 = 174682.74

and so on till 360 payments