Question

1. An amount of money doubles in size after nine years when invested at eight percent interest. The rate with continuous compounding that an amount will double in just half the time taken at the aforementioned eight percent rate is closest to:

2. A new method of training inexperienced sewing-machine operators is proposed to a wearing-apparel firm. The consultants claim that this program can save $7,000 per year over the planned 5-year life of the project with an immediate investment cost of $12,000. The annual training expenses will be $4,000. Using a 6 percent annual interest rate, the present value of the amount of money that this program can save the company is closest to:

Answer 1

Question 1

For continuous compounding, time value of money function is:

FV = PV * e^rt

Based on question, FV = 2PV, t = 9/2 years = 4.5 years

2PV = PV * e^{(r * 4.5)}

2 = e^{(r * 4.5)}

Taking natural log on both sides

LN (2) = 4.5r

r = 0.6931/4.5

r = 0.1540

Hence Rate = 15.40%

Q2

Annual saving = $7000

Annual training Expense = $4000

Net saving = $3000

r = 6%, n = 5 years

PV of savings is calculable by using the PV of annuity function, which is:

P = $3000, r = 6%, n = 5

PV = 3000 * 4.2124

PV = $12,637.09

{If the question qould have asked us for NPV, NPV = $12,637.09 - $12,000 = $637.09}