Question

Amortized loans :

You are faced with a choice of mortgage terms to purchase a new home costing $300,000. You are able to put a $40,000 down payment on the home. The bank offers you a fixed-rate of 4.5% for a 30-year loan, and one at 4% for a 15-year loan. You have determined that you can afford up to, but not more than, a $1750 monthly mortgage payment. How do the payment amounts on the 2 loans compare? Can you afford the 15-year loan?

Answer 1

Cost of home = $300,000

Funds available for down payment of home = $40,000

Therefore required loan = Cost - down payment = $300,000 - $40,000

Therefore required loan (PV) = $260,000

Option 1: 30 year loan with 4.5% rate

Loan amount (PV) = $260,000

Monthly rate of interest (I) = 4.5%p.a. / 12 = 0.375% p.m.

No of monthly installments to be paid (N) = 30 years x 12 = 360 installments

Monthly Installment amount (PMT) = ?

Using financial calculator or PMT function in excel,

Monthly Installment amount (PMT) = $1317.38

Option 1: 15 year loan with 4% rate

Loan amount (PV) = $260,000

Monthly rate of interest (I) = 4%p.a. / 12 = 0.3333% p.m.

No of monthly installments to be paid (N) = 15 years x 12 = 180 installments

Monthly Installment amount (PMT) = ?

Using financial calculator or PMT function in excel,

Monthly Installment amount (PMT) = $1923.19

Maximum monthly payment amount I can afford = $1750.

Therefore I cannot afford to opt for 15year loan.

Thumbs up please if satisfied. Thanks :)

Comment if further doubts in above.