Question

What is the end of year wealth for Jane Christine if she receives an annual interest rate of 24% compounded monthly on a $1 investment?

		$ 1.6531
		$ 1.2682
		$1.24
		$ 1.987

Your firm is purchasing a new telephone system that will last for four years. You can purchase the system for an up-front cost of $150,000, or you can lease the system from the manufacturer for $4,000 paid at the end of each month. The lease price is offered for a 48-month lease with no early termination – you cannot end the lease early. Your firm can borrow at an interest rate of 6% APR with monthly compounding. Should you purchase the system outright by paying $150,000 now or pay $4,000 per month?

		You should choose to pay $4,000 per month.
		You should choose to purchase the system outright by paying the upfront cost of $150,000.
		You can either choose to purchase the system outright by paying the upfront cost of $150,000 or choose to pay $4,000 per month, because the present values of these two choices are the same.
		None

Answer 1

The amount is computed as shown below:

Future value = Present value x (1 + r)ⁿ

= $ 1 x (1 + 0.24 / 12) ^{12 x 1}

r is divided by 12 and n is multiplied by 12, since the interest is compounded monthly.

= $ 1 x 1.02 ¹²

= $ 1.2682 Approximately

The present value of the leasing alternative is computed as shown below:

Present value = Monthly payment x [ (1 – 1 / (1 + r)ⁿ) / r ]

r is computed as follows:

= 6% / 12 (Since the interest is compounded monthly, hence divided by 12)

= 0.5% or 0.005

So, the present value will be computed as follows:

= $ 4,000 x [ (1 - 1 / (1 + 0.005)⁴⁸ ) / 0.005 ]

= $ 4,000 x 42.58031778

= $ 170,321.2711

The present value of upfront value of $ 150,000 will be $ 150,000 since it is paid upfront or today.

So, the correct answer is option of You should choose to purchase the system outright by paying the upfront cost of $150,000 since the present value of cost of paying upfront is less than the present value of cost of leasing alternative.

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