Question

Your finance textbook sold 53,000 copies in its first year. The publishing company expects the sales to grow at a rate of 15 percent each year for the next three years and by 10 percent in the fourth year. Calculate the total number of copies that the publisher expects to sell in years 3 and 4. (If you solve this problem with algebra, round intermediate calculations to 6 decimal places. In all cases, round your final answers to the nearest whole number.)

Number of copies sold in 3 years_____
Number of copies sold in 4 years_____

Answer 1

To calculate the expected sales for the third and fourth years, compound growth rates were applied to the initial sales figure. Approximately 80,613 copies are expected to be sold in the third year, and 88,674 copies in the fourth year.

Step-by-step explanation:

The question is asking to calculate the total number of copies that the publisher expects to sell in the third and fourth years, given an initial sales number and growth rates for each year. We must apply the compound growth formula to find the expected sales after three and four years.

Initial sales in the first year: 53,000 copies
Growth rate for the next three years: 15% annually
Growth rate for the fourth year: 10%

To calculate the sales for the third year, we use the formula: A = P(1 + r)^n
Where A is the amount after n years, P is the initial amount, r is the growth rate, and n is the number of years.

For year 3 sales:
P = 53,000 copies
r = 15% = 0.15
n = 3 years

A = 53,000(1 + 0.15)^3

Calculating the amount:
A = 53,000(1.15)^3
A = 53,000(1.521)
A = approximately 80,613 copies

For year 4 sales:
Now we take the amount at the end of year 3 and apply a growth rate of 10% for the fourth year.

A = 80,613(1 + 0.10)
A = 80,613(1.10)
A = approximately 88,674 copies

Therefore, the publisher expects to sell approximately 80,613 copies in the third year, and 88,674 copies in the fourth year.