Ray’s company borrows $5,000 from the local bank to invest in a personal computer for the quality control department on the term that the company will pay back $1,200 each year for the next 5 years. The first payment is due on the first loan anniversary. What interest rate the bank is charging, if

Question

Ray’s company borrows $5,000 from the local bank to invest in a personal computer for the quality control department on the term that the company will pay back $1,200 each year for the next 5 years. The first payment is due on the first loan anniversary. What interest rate the bank is charging, if compounding is annual?

Accepted Answer

First, we need to decide whether to sketch a cashflow diagram to facilitate problem comprehension. If you can comprehend without the diagram, there is no need to sketch it, since it is not being specifically asked for. However, if the diagram will help you, then sketch it. Let us say that we can do without the [latex]diagram^{14}[/latex].

Note that the problem involves six cashflows; in other words, multi-payment analysis of this chapter is applicable. Next, we need to check whether the payments are irregular or regular. The five $1,200 payments are regular, each being annual. Next, do they follow a pattern? The answer is yes, and the pattern is uniform series since the payments are
equal. Thus, the discussions of Section 4.3.2 are applicable, with Equation (4.3b) being the relevant formula for the functional notation method.

We next gather the given values of the parameters and proceed. These are: P = $5,000, A = $1,200, n = 5. With n in years, the unknown [latex]i[/latex] will get evaluated as annual. Let us say that we decide to use the functional notation method. Thus, from Equation (4.3b),

[latex]A=P({A}/{P},i,5)[/latex]

[latex]1,200=5,000({A}/{P},i,5)[/latex]

[latex]({A}/{P},i,5)={1,200}/{5,000}[/latex]

[latex]=0.24[/latex]

Searching in the tables under the proper column following the procedure explained in Example 3.8, we find that

[latex]({P}/{A},i,5)=0.2374[/latex] , for [latex]i = 6\% [/latex] ,and

[latex]=0.2439[/latex] , for [latex]i = 7\%[/latex]

Conducting the interpolation as explained in Example 3.8, we get in this case

[latex]\frac{0.24-0.2374}{0.2439-0.2374} -\frac{af}{7-6}[/latex]

[latex]af=\frac{0.0026}{0.0065}[/latex]

[latex]=0.4[/latex]

Therefore, [latex]i=6\% + 0.4[/latex]

[latex]=6.4\%[/latex]

Thus, the bank is charging Ray’s company an annual interest rate of approximately 6.4%.

Question 4.3: Ray’s company borrows $5,000 from the local bank to invest i...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions