A woman inherits $10,000, and is considering where to invest it.

Question

Calculate the annual rates of return for each of the following investments (rounding to the nearest 0.1% where needed).

 

a) She has a $15,000 car loan, on which she is charged an annual yield of 7.9%. She could reduce this debt to $5,000.

Rate of Return:

 

b) She can loan the money to a relative’s business, who promises to pay her back $15,000 in 6years (Assume this loan is safe—she’s 100% certain that she’ll be paid back).

Rate of Return:

 

c) She can purchase a parking space for her car which costs $10,000. Each month she must pay $15 in taxes and another $15 for maintenance, but she no longer has to pay $100per month to park her car in a garage.

Rate of Return:

Answer 1

There is some confusion here, as Return on Investment is generally defined as the money that a person or company earns as a percentage of the total value of the assets that are invested. It is calculated by
Return on investment = (Income - Cost) / Cost

Because it is easy to calculate the return on investment, it is a common measure of the profitability of an investment.

decisions.

 

Return on Investment is not generally used to measure the benefit of reducing expenses as items 1 and 3 describe. That being said, let's look at the three questions.

 

a. The only benefit here is an avoidance of interest expense. So, we must look at the difference between the interest charged on $15000 less the interest charged on $10000. Since no time frame was stated, we can only use 1 year as the basis for the calculation. We know that Interest  = Principal x Rate x Time. In this case, Interest reduction = ($15000 • 0.079) - ($10,000 • 0.079) = $1185 - $790 = $395. When that number is divided by $10000, we get a "return" of 3.95%

 

b. Here, an actual return is possible, and the formula gives ($15000 - 10000)/$10000 = .5 = 50%. But we have to average that number over 5 years, so the average return will be 10%.

 

c. Here, we have an expense reduction, but there is a possible asset acquisition also. The expense reduction is [($15 + 15 + 100)•12]/$10000 = 15.6%. No details were given on the parking space.