Question

1.

Sawyer Corporation's 2017 sales were $12 million. Its 2012 sales were $6 million.

At what rate have sales been growing? Round your answer to two decimal places.

%

Suppose someone made this statement: "Sales doubled in 5 years. This represents a growth of 100% in 5 years, so, dividing 100% by 5, we find the growth rate to be 20% per year." Is the statement correct?

a. correct because 100% divided by 5 equals 20%.

b. incorrect because there are 6 years of sales growth between 2012 and 2017.

c. incorrect because a company's sales cannot double in such a short time span.

d. incorrect since the effect of compounding is not considered.

e. correct since the effect of discounting is considered.

2.

Find the interest rates earned on each of the following. Round your answers to the nearest whole number.

You borrow $650 and promise to pay back $754 at the end of 1 year.

%

You lend $650 and the borrower promises to pay you $754 at the end of 1 year.

%

You borrow $67,000 and promise to pay back $127,187 at the end of 11 years.

%

You borrow $11,000 and promise to make payments of $3,359.50 at the end of each year for 5 years.

Answer 1

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

1.

12=6(1+r/100)^5

(12/6)^(1/5)=(1+r/100)

(1+r/100)=1.1487

r=(1.1487-1)*100

=14.87%(Approx)

Hence the statement is incorrect because the effect of compounding is not considered.(compounding effect takes into account the 'interest earned on interest factor' ](D).

2.

a.754=650(1+r/100)^1

(754/650)^(1)=1+r/100

1+r/100=1.16

r=(1.16-1)*100

=16%

b.754=650(1+r/100)^1

(754/650)^(1)=1+r/100

1+r/100=1.16

r=(1.16-1)*100

=16%

c.

127187=670001+r/100)^11

(127187/67000)^(1/11)=1+r/100

1+r/100=1.06

r=(1.06-1)*100

=6%(Approx)

4.

Let interest rate be x%

At this rate;present value of payments=11000
11000=3359.50/1.0x+3359.50/1.0x^2+...............+3359.50/1.0x^5

Hence x=interest rate=16%