Question

Problem 2 A new machine is expected to cost $6000 and have a life of 5 years. Maintenance costs will be $1700 the first year, second year, and the third year, while in the fourth year and fifth year, the maintenance costs are $2100 and $2300 respectively. How much should be budgeted and deposited now, to pay and handle the maintenance costs for this machine in an account that earns: a) 20% per year compounded quarterly b) 16% per year compounded monthly,

help part A and B

Answer 1

A.

Effective annual interest rate = (1+20%/4)^4 - 1 = 21.5506%

Then,

PW of the maintenance cost = 1700*(1-1/(1+21.5506%)^3)/21.5506% + 2100/(1+21.5506%)^4 + 2300/(1+21.5506%)^5

PW of the maintenance cost = $5324.73 or $5325

So, $5324.73 or $5325 should be kept in the account to cover the maintenance cost.

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B.

Effective annual interest rate = (1+16%/12)^12 - 1 = 17.2271%

Then,

PW of the maintenance cost = 1700*(1-1/(1+17.2271%)^3)/17.2271% + 2100/(1+17.2271%)^4 + 2300/(1+17.2271%)^5

PW of the maintenance cost = $5893.46 or $5893

So, $5893.46 or $5893 should be kept in the account to cover the maintenance cost.