Question

A borrower is interested in comparing the monthly payments on two otherwise equivalent 30 year FRMs. Both loans are for $100,000 and have a 7% interest rate. Loan 1 is fully amortizing, where as Loan 2 has negative amortization with a $120,000 balloon payment due at the end of the life of the loan. How much higher is the monthly payment on loan 1 versus loan 2

Answer 1

Answer:

The monthly payment in Loan 1 is higher than in loan 2 by:

(665.30 - 566.94) = $98.36

Explanation:

Solution:

Comparison of Loan 1 and Loan 2 in terms of monthly payments.

For the first loan, we have to calculate equal monthly payments with the following details:

Principal = $ 100,000,

Monthly Interest rate = 7/12 = 0.58% ,

Term = 360 months

Use the PV = C (1 - (1+r)-n ) / r ,

where PV = Principal, r = monthly rate, n = 360 and

find C (EMI) = $665.30

NOTE: (Excel function is used: PMT(rate, year, PV) formula for convenience)

For Loan 2, we have to understand a few things.

The original loan principal is $ 100,000,

but you are allowed to do a balloon payment of $ 120000 at the end of 30 years.

The present value of the Balloon payment can be deducted from the principal to find out the monthly cash payments to be done.

The monthly payments will of course be lower since a lump sum balloon payment is done at the end.

The calculation is similar to the above. In this scenario, the Monthly payment comes out to be $ 566.94

Hence,

The monthly payment in Loan 1 is higher than in loan 2 by:

(665.30 - 566.94) = $98.36