Questions: Find i (the rate per period) and n (the number of periods) for the following annuity. Annual deposits of 1,500 are made for 12 years into an annuity that pays 6.65% compounded annually. i= (Type an integer or a decimal.) n=

Find i (the rate per period) and n (the number of periods) for the following annuity. Annual deposits of 1,500 are made for 12 years into an annuity that pays 6.65% compounded annually.

i= (Type an integer or a decimal.)
n=

Transcript text: Find i (the rate per period) and n (the number of periods) for the following annuity. Annual deposits of $\$ 1,500$ are made for 12 years into an annuity that pays $6.65 \%$ compounded annually. \[ \begin{array}{l} \mathrm{i}=\square \text { (Type an integer or a decimal.) } \\ \mathrm{n}=\square \end{array} \]

Solution

Solution Steps

To find the rate per period (i) and the number of periods (n) for the given annuity, we need to use the information provided:

Annual deposits of $1,500
Duration of 12 years
Interest rate of 6.65% compounded annually

The rate per period (i) is simply the annual interest rate, and the number of periods (n) is the number of years.

Solution Approach

The rate per period (i) is the annual interest rate given, which is 6.65%.
The number of periods (n) is the number of years the deposits are made, which is 12 years.

Step 1: Determine the Rate per Period

The annual interest rate given for the annuity is $ 6.65\% $. To express this as a decimal, we convert it by dividing by $ 100 $: \[ i = \frac{6.65}{100} = 0.0665 \]

Step 2: Determine the Number of Periods

The number of years for which the deposits are made is $ 12 $. Therefore, the number of periods is: \[ n = 12 \]