Chapter 8, Problem 17CR

To determine

To describe: the first eight terms of the sequence and their significance.

Answer to Problem 17CR

First eight terms of the sequence are as follows

  $\underset{\_}{3015,3030.075,3045.225,3060.451,3075.754,3091.132,3106.588,3122.121}$ , which represents balance in account after first eight quarters.

Explanation of Solution

Given information:

The sequence representing balance in the account after $n$ quarters when initial deposited amount is $3000 and rate of interest is 2% compounded quarterly is as follows

  $A_n=3000{\left(1+\frac{0.02}{4}\right)}^n$

Calculation:

Need to calculate first 8 term of following sequence.

  $A_n=3000{\left(1+\frac{0.02}{4}\right)}^n$

  $=3000{\left(\frac{4+0.02}{4}\right)}^n$

  $=3000{\left(1.005\right)}^n$

Calculate first term by substituting $n=1$ .

  $A_1=3000{\left(1.005\right)}^1=3015$

Calculate second term by substituting $n=2$ .

  $A_2=3000{\left(1.005\right)}^2=3030.075$

Calculate third term by substituting $n=3$ .

  $A_3=3000{\left(1.005\right)}^3=3045.225$

Calculate fourth term by substituting $n=4$ .

  $A_4=3000{\left(1.005\right)}^4=3060.451$

Calculate fifth term by substituting $n=5$ .

  $A_5=3000{\left(1.005\right)}^5=3075.754$

Calculate sixth term by substituting $n=6$ .

  $A_6=3000{\left(1.005\right)}^6=3091.132$

Calculate seventh term by substituting $n=7$ .

  $A_7=3000{\left(1.005\right)}^7=3106.588$

Calculate eight term by substituting $n=8$ .

  $A_8=3000{\left(1.005\right)}^8=3122.121$

First eight terms of the sequence represents balance in account after first eight quarters.

Hence first eight terms of the sequence are as follows

  $\underset{\_}{3015,3030.075,3045.225,3060.451,3075.754,3091.132,3106.588,3122.121}$ , which represents balance in account after first eight quarters.