A restaurant manager has the option of a 30-year loan of $415,000 at an annual interest rate of 3.75% or the same interest rate but on a loan for 15 years.
(a)
Calculate the monthly payment for each loan. (Round your answers to the nearest cent.)
30-year $ ?
15-year $ ?
(b)
Calculate the savings in interest by using the 15-year loan. (Round your answer to the nearest cent.)
(c)
The term of the 15-year loan is one-half the term of the 30-year loan. Is the monthly payment for the 15-year loan twice that of the 30-year loan?
(d)
Is the interest savings for the 15-year loan more or less than one-half of the interest paid on the 30-year loan?
(a)
For the 30-year loan:
Monthly interest rate = 3.75% / 12 = 0.3125%
Number of months = 30 * 12 = 360
Monthly payment = $415,000 * (0.003125 / (1 - (1 + 0.003125)^(-360))) = $1,915.58
For the 15-year loan:
Monthly interest rate = 3.75% / 12 = 0.3125%
Number of months = 15 * 12 = 180
Monthly payment = $415,000 * (0.003125 / (1 - (1 + 0.003125)^(-180))) = $2,999.85
(b)
Interest paid on 30-year loan = $1,915.58 * 360 - $415,000 = $252,809.53
Interest paid on 15-year loan = $2,999.85 * 180 - $415,000 = $143,973.74
Savings in interest = $252,809.53 - $143,973.74 = $108,835.79
(c)
The monthly payment for the 15-year loan is not twice that of the 30-year loan. It is actually higher.
(d)
The interest savings for the 15-year loan is less than one-half of the interest paid on the 30-year loan.