Question

Mr. and Mrs. Spirit purchased a $35,000 home 20 years ago. They took a 30- year mortgage for $30,000 at a 3% annual interest rate. Their bank, the First Amityville National Bank, has recently offered the Spirits two alternative by which they could prepay their mortgage. The Spirits have just made their 20th annual payment. Under the first alternative, the Spirits could prepay their mortgage at a 30% discount from the current principal outstanding. If current 10-year mortgage rates are 12%, should the Spirits accept the offer? Ignore taxes and assume payments are made at the end of each year (instead of monthly). The second alternative would replace their existing mortgage with a five-year zero-interest loan, in the amount of their current mortgage’s principal outstanding. This new loan was to be repaid in 5 equal annual payments. The banker pointed out that this option would “save them well over $2,000 in interest”.

Answer 1

Annual Installment of old loan = loan amount / PVIFA

= 30000 / PVIFA (3%, 30 years)

= 30000/ 19.6004

= $1530.58

Loan amount outstanding = annual installment * PVIFA ( 3%,10 years)

= 1530.58 * 8.5302

= $13056.15

OFFER 1 - 30% discount

Amount to be repaid = 13056.15 * (1-0.30)

= $9139.31

10 year mortgage rate is 12%

thus value of loan outstanding at 12% = 1530.58 * PVIFA ( 12%, 10years)

= 1530.58 * 5.6502

= $ 8648.08

Since the amount to be paid out under the option is more than the value of loan outstanding thus offer should not be opted.

OFFER 2

amount to be repaid under five year zero interest loan = $13056.16

it will be paid in 5 equal annual installments of = 13056.16/5 = $2611.23 per year

Annual installment if loan is taken interest rate @ 12% = 13056.16/ PVIFA (12%, 5years)

= 13056.16 / 3.6048

= $ 3621.88 per year

current value of loan under this option with interest rate @ 12% = 2611.23* 3.6048

= $ 9412.96

Since the amount to be repaid under option 2 is less it should be accepted