Miller Machining needs to purchase a piece of machinery to be able to compete on
ID: 1188204 • Letter: M
Question
Miller Machining needs to purchase a piece of machinery to be able to compete on a new contract with a first-tier automotive supplier. The machinery will cost $140,000, and the owner arranges to borrow the entire amount at 8 percent interest. The initial payment 1 year after purchase is $11,000 with successive payments increasing each year by $X. The last payment is to be made 6 years afer the purchase.
a) By how much ($X) does the payment increase each year?
b) What is the amount of the final payment?
c) Suppose that, at the last minute, the company decides to purchase the same machinery at the same rate (8 percent), with payments decreasing by $7,500 each year. How much is the first payment?
Explanation / Answer
140,000 = 11000/1.08 + ( 11000 + x ) / 1.08^2 + ... + ( 11000 + 5x ) /1.08^6
140,000 = ( 11000/1.08 + 11000/1.08^2 +... + 11000/1.08^6 ) + x ( 1/1.08^2 + 2/1.08^3 + .... + 5/1.08^6 )
140,000 = 50851.68 + x * ( 10.52 )
a) x = 8471.54
b) amount of final payment = 11000 + 5 * x = 53357.69
c)
140000 = y/1.08 + ( y - 7500 ) /1.08^2 + ( y - 15000 ) / 1.08^3 + ... + ( y - 37500 )/ 1.08^6
140000 = y * ( 1/1.08 + 1/1.08^2 + ... + 1/1.08^6 ) - 7500( 1/1.08^2 + ... + 5/1.08^6 )
140000 = 4.62 * y - 7500 * 10.52
y = 47356.75
Hence the first payment is $47,356.75