Chapter 12, Problem 1CR

Payment or receipt of equal amounts of money per period for a specified amount of time is known as a(n) ____ (12-1)

To determine

To fill: The blank given in the statement “Payment or receipt of equal amounts of money per period for a specified amount of time is known as __________.”

Answer to Problem 1CR

Solution:

Payment or receipt of equal amounts of money per period for a specified amount of time is known as Annuity.

Explanation of Solution

Payment or receipt of equal amounts of money per period for a specified amount of time is known as Annuity.

The formula to compute the present value of annuity due is,

$PV=Pmt\times \frac{1-{\left(1+i\right)}^{-n}}{i}\times \left(1+i\right)$

Where, PV is the future value, Pmt is the Annuity payment, i is the interest rate per period, n is the number of periods.

For example:

Consider that Annuity payment amount is $\$3,500$, frequency of payment is $3$ month, time duration is $4$ years, nominal rate of return is $3\%$ and interest is compounded quarterly.

The rate period is $0.75\%\left(3\%÷4\text{ period per year}\right)$.

The number of periods is $16\left(\text{4 years}\times 4\text{ period per year}\right)$.

Substitute $16$ for number of periods, $0.0075$ for interest rate per period, $\$3,500$ for Pmt in the formula $PV=Pmt\times \frac{1-{\left(1+i\right)}^{-n}}{i}\times \left(1+i\right)$ as;

$\begin{array}{c}PV=3,500\times \frac{1-{\left(1+0.0075\right)}^{-16}}{0.0075}\times \left(1+0.0075\right)\\ =3,500\times \frac{1-{\left(1.0075\right)}^{-16}}{0.0075}\times 1.0075\\ =3,500\times \frac{0.11268234}{0.0075}\times 1.0075\\ =\$52,979.48\end{array}$

Hence, present value of annuity due is $\$52,979.48$.