Question

For each of the following cases, indicate (a) to what rate columns, and (b) to what number of periods you would refer in looking up the interest factor.

1. In a future value of 1 table Annual Number of Rate Years Invested Compounded

a. 9% 9 Annually b. 12% 5 Quarterly c. 10% 15 Semiannually

2. In a present value of an annuity of 1 table Annual Number of Number of Frequency of Rate Years Involved Rents Involved Rents

a. 9% 25 25 Annually b. 10% 15 30 Semiannually c. 12% 7 28 Quarterly

Short answer

The ROI and number of the period for 1a is 9%,9; 1b is 3%, 20; 1c is 5%, 30 and for 2a is 9%, 25; 2b is 5%, 30; 2c is 3%, 28

Step-by-step solution

Computation of rate of interest and number of periods

a)

$\begin{array}{rcl}\mathrm{Rate}\mathrm{of}\mathrm{interest}& =& 9\%\\ \mathrm{Number}\mathrm{of}\mathrm{periods}& =& 9\end{array}$

b)

$\begin{array}{rcl}\mathrm{Rate}\mathrm{of}\mathrm{interest}& =& \frac{12\%}{4}\\ & =& 3\%\\ \mathrm{Number}\mathrm{of}\mathrm{periods}& =& 5\times 4\\ & =& 20\\ & & \end{array}$

c)

role="math" localid="1648277140382" $\begin{array}{rcl}\mathrm{Rate}\mathrm{of}\mathrm{interest}& =& \frac{10\%}{4}\\ & =& 5\%\\ \mathrm{Number}\mathrm{of}\mathrm{periods}& =& 15\times 2\\ & =& 30\end{array}$

Calculation of interest rate and number of periods

2.

a)

$\begin{array}{rcl}\mathrm{Rate}\mathrm{of}\mathrm{interest}& =& 9\%\\ \mathrm{Number}\mathrm{of}\mathrm{periods}& =& 25\end{array}$

b)

$\begin{array}{rcl}\mathrm{Rate}\mathrm{of}\mathrm{interest}& =& \frac{10\%}{4}\\ & =& 5\%\\ \mathrm{Number}\mathrm{of}\mathrm{periods}& =& 15\times 2\\ & =& 30\end{array}$

c)

$\begin{array}{rcl}\mathrm{Rate}\mathrm{of}\mathrm{interest}& =& \frac{12\%}{4}\\ & =& 3\%\\ \mathrm{Number}\mathrm{of}\mathrm{periods}& =& 7\times 4\\ & =& 28\end{array}$