Question 1

Choose the one alternative that best completes the statement or answers the question.
Find the effective rate of interest.
-$6 \frac { 1 } { 4 } \%$ compounded monthly
A) $6.43 \%$
B) $6.25 \%$
C) $6.39 \%$
D) $6.29 \%$

Accepted Answer

The effective rate of interest can be calculated using the formula $ (1 + \frac{r}{n})^n - 1 $, where $ r $ is the annual nominal rate (as a decimal) and $ n $ is the number of compounding periods per year. For $ 6 \frac{1}{4} \% = 6.25 \% $ compounded monthly, $ r = 0.0625 $ and $ n = 12 $. Plugging these values into the formula gives an effective rate of approximately $ 6.43\% $.

Question 2

Choose the one alternative that best completes the statement or answers the question.
Find the effective rate of interest.
-12.25% compounded monthly
A) 12.962%
B) 12.373%
C) 13.155%
D) 12.455%

Accepted Answer

The effective rate of interest, when interest is compounded monthly, can be calculated using the formula $ (1 + \frac{r}{n})^{n} - 1 $, where $ r $ is the annual nominal rate (as a decimal) and $ n $ is the number of compounding periods per year. For 12.25% compounded monthly, $ r = 0.1225 $ and $ n = 12 $. Plugging these values into the formula gives $ (1 + \frac{0.1225}{12})^{12} - 1 \approx 0.12962 $ or 12.962% when converted to a percentage.

Question 3

Find the present value. Round to the nearest cent.
-To get $10,500 after7 years at 4% compounded annually
A) $8,298.30
B) $2,520.86
C) $7,599.18
D) $7,979.14

Accepted Answer

The answer of Find the present value. Round to the...

Question 4

Choose the one alternative that best completes the statement or answers the question.
Find the effective rate of interest.
-25.12% compounded daily
A) 25.243%
B) 25.325%
C) 26.025%
D) 28.546%

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 5

Write the word or phrase that best completes each statement or answers the question.
-$$4 \frac { 3 } { 4 } \% \text { compounded quarterly }$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 6

Find the present value. Round to the nearest cent.
-To get $6500 after 6 years at 7% compounded quarterly
A) $2,213.65
B) $4,331.22
C) $4,361.36
D) $4,286.35

Accepted Answer

The answer of Find the present value. Round to the...

Question 7

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-Which of the two rates would yield the larger amount in 1 year: $9 \%$ compounded monthly or $9 \frac { 1 } { 4 } \%$ compounded annually?
A) $9 \%$ compounded monthly
B) $9 \frac { 1 } { 4 } \%$ compounded annually
C) They will yield the same amount.

Accepted Answer

The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount, $P$ is the principal, $r$ is the annual interest rate, $n$ is the number of times the interest is compounded per year, and $t$ is the time in years. For $9\%$ compounded monthly, $r = 0.09$, $n = 12$, and $t = 1$. For $9\frac{1}{4}\%$ compounded annually, $r = 0.0925$, $n = 1$, and $t = 1$. Calculating both, the $9\%$ compounded monthly yields a larger amount due to the effect of monthly compounding.

Question 8

Solve the problem.
-What principal invested at 8% compounded continuously for 4 years will yield $1190? Round the answer to two decimal places.
A) $1638.78
B) $1188.62
C) $864.12
D) $627.48

Accepted Answer

The formula for continuous compounding is $A = Pe^{rt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount, $r$ is the annual interest rate (decimal), $t$ is the time the money is invested for in years, and $e$ is the base of the natural logarithm, approximately equal to 2.71828. Given $A = 1190$, $r = 0.08$, and $t = 4$, we solve for $P$: $1190 = Pe^{(0.08)(4)}$. Solving for $P$ gives approximately $P = 864.12$.

Question 9

Write the word or phrase that best completes each statement or answers the question.
-What principal invested at 6%, compounded continuously for 3 years, will yield $1500? Round the answer to
two decimal places.

Accepted Answer

The answer of Write the word or phrase that best...

Question 10

Choose the one alternative that best completes the statement or answers the question.
-How much money needs to be invested now to get $2000 after 4 years at 8% compounded quarterly? Express your answer to the nearest dollar.
A) $2746
B) $1848
C) $1457
D) $584

Accepted Answer

To find the present value, use the formula for compound interest: $ P = \frac{A}{(1 + \frac{r}{n})^{nt}} $, where $ A = 2000 $, $ r = 0.08 $, $ n = 4 $, and $ t = 4 $. Plugging in these values gives $ P = \frac{2000}{(1 + \frac{0.08}{4})^{4 \times 4}} \approx 1457 $.

Question 11

Choose the one alternative that best completes the statement or answers the question.
Find the effective rate of interest.
-12% compounded continuously
A) 12.75%
B) 12.089%
C) 12.451%
D) 12.374%

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 12

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-A local bank advertises that it pays interest on savings accounts at the rate of 3% compounded monthly. Find the effective rate. Round answer to two decimal places.
A) 3.04%
B) 36%
C) 3.40%
D) 3.44%

Accepted Answer

The effective annual rate (EAR) can be calculated using the formula: EAR = (1 + i/n)^(n*t) - 1, where i is the nominal rate (0.03), n is the number of compounding periods per year (12), and t is the number of years (1). Plugging in the values, EAR = (1 + 0.03/12)^(12*1) - 1 = 0.0304 or 3.04%.

Question 13

Find the present value. Round to the nearest cent.
-To get $10,000 after 3 years at 6% compounded monthly
A) $10,616.78
B) $8,356.45
C) $3,333.33
D) $9,419.05

Accepted Answer

The present value (PV) can be calculated using the formula PV = FV / (1 + r/n)^(nt), where FV is the future value ($10,000), r is the annual interest rate (6% or 0.06), n is the number of times the interest is compounded per year (12 for monthly), and t is the time in years (3). Plugging in the values: PV = $10,000 / (1 + 0.06/12)^(12*3) = $8,356.45.

Question 14

Choose the one alternative that best completes the statement or answers the question.
Find the effective rate of interest.
-11.8% compounded continuously
A) 12.174%
B) 12.251%
C) 11.889%
D) 12.524%

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 15

Find the present value. Round to the nearest cent.
-To get $2000 after 10 years at 9% compounded semiannually
A) $1,170.71
B) $866.60
C) $829.29
D) $844.82

Accepted Answer

The present value is calculated using the formula $ PV = \frac{FV}{(1 + \frac{r}{n})^{nt}} $, where $ FV = 2000 $, $ r = 0.09 $, $ n = 2 $, and $ t = 10 $. Plugging in these values gives $ PV = \frac{2000}{(1 + \frac{0.09}{2})^{2 \times 10}} \approx 829.29 $.

Question 16

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-Which of the two rates would yield the larger amount in 1 year: 5.2% compounded monthly or 5.1% compounded daily?
A) 5.2% compounded monthly
B) 5.1% compounded daily
C) They will yield the same amount.

Accepted Answer

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years. Compounding more frequently at a slightly lower rate (5.1% daily) does not necessarily yield more than a slightly higher rate compounded less frequently (5.2% monthly). The 5.2% compounded monthly will yield a larger amount due to the higher interest rate despite the less frequent compounding compared to 5.1% compounded daily.

Question 17

Choose the one alternative that best completes the statement or answers the question.
Find the effective rate of interest.
-5.5% compounded quarterly
A) 6.405%
B) 5.623%
C) 5.614%
D) 5.705%

Accepted Answer

The effective rate of interest can be calculated using the formula: $ (1 + \frac{r}{n})^n - 1 $, where $ r $ is the nominal rate and $ n $ is the number of compounding periods per year. For 5.5% compounded quarterly, $ r = 0.055 $ and $ n = 4 $. The calculation gives approximately 5.614%.

Question 18

Find the present value. Round to the nearest cent.
-To get $5600 after 8 years at 5% compounded annually
A) $3,639.62
B) $2,260.9
C) $5,962.67
D) $3790.30

Accepted Answer

The answer of Find the present value. Round to the...

Question 19

Find the present value. Round to the nearest cent.
-To get $25,000 after 6 years at 10% compounded semiannually
A) $14,616.98
B) $13,920.94
C) $14,111.85
D) $11,079.06

Accepted Answer

The answer of Find the present value. Round to the...

Question 20

Write the word or phrase that best completes each statement or answers the question.
-Carla has just inherited a building that is worth $250,000. The building is in a high demand area, and the value
of the building is projected to increase at a rate of 25% per year for the next 4 years. How much more money
will she make if she waits four years to sell the building instead of selling now?

Accepted Answer

The answer of Write the word or phrase that best...

Quiz 4: Exponential and Logarithmic Functions

Choose the one alternative that best completes the statement or answers the question. Find the effective rate of interest. - $6 \frac { 1 } { 4 } \%$ compounded monthly

Choose the one alternative that best completes the statement or answers the question. Find the effective rate of interest. -12.25% compounded monthly

Find the present value. Round to the nearest cent. -To get $10,500 after7 years at 4% compounded annually

Choose the one alternative that best completes the statement or answers the question. Find the effective rate of interest. -25.12% compounded daily

Write the word or phrase that best completes each statement or answers the question. - $4 \frac { 3 } { 4 } \% \text { compounded quarterly }$

Find the present value. Round to the nearest cent. -To get $6500 after 6 years at 7% compounded quarterly

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Which of the two rates would yield the larger amount in 1 year: $9 \%$ compounded monthly or $9 \frac { 1 } { 4 } \%$ compounded annually?

Solve the problem. -What principal invested at 8% compounded continuously for 4 years will yield $1190? Round the answer to two decimal places.

Write the word or phrase that best completes each statement or answers the question. -What principal invested at 6%, compounded continuously for 3 years, will yield $1500? Round the answer to two decimal places.

Choose the one alternative that best completes the statement or answers the question. -How much money needs to be invested now to get $2000 after 4 years at 8% compounded quarterly? Express your answer to the nearest dollar.

Choose the one alternative that best completes the statement or answers the question. Find the effective rate of interest. -12% compounded continuously

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -A local bank advertises that it pays interest on savings accounts at the rate of 3% compounded monthly. Find the effective rate. Round answer to two decimal places.

Find the present value. Round to the nearest cent. -To get $10,000 after 3 years at 6% compounded monthly

Choose the one alternative that best completes the statement or answers the question. Find the effective rate of interest. -11.8% compounded continuously

Find the present value. Round to the nearest cent. -To get $2000 after 10 years at 9% compounded semiannually

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Which of the two rates would yield the larger amount in 1 year: 5.2% compounded monthly or 5.1% compounded daily?

Choose the one alternative that best completes the statement or answers the question. Find the effective rate of interest. -5.5% compounded quarterly

Find the present value. Round to the nearest cent. -To get $5600 after 8 years at 5% compounded annually

Find the present value. Round to the nearest cent. -To get $25,000 after 6 years at 10% compounded semiannually

Quiz 4: Exponential and Logarithmic Functions

Choose the one alternative that best completes the statement or answers the question. Find the effective rate of interest. - 614%6 \frac { 1 } { 4 } \%641​% compounded monthly

Choose the one alternative that best completes the statement or answers the question. Find the effective rate of interest. -12.25% compounded monthly

Find the present value. Round to the nearest cent. -To get $10,500 after7 years at 4% compounded annually

Choose the one alternative that best completes the statement or answers the question. Find the effective rate of interest. -25.12% compounded daily

Write the word or phrase that best completes each statement or answers the question. - 434% compounded quarterly 4 \frac { 3 } { 4 } \% \text { compounded quarterly }443​% compounded quarterly

Find the present value. Round to the nearest cent. -To get $6500 after 6 years at 7% compounded quarterly

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Which of the two rates would yield the larger amount in 1 year: 9%9 \%9% compounded monthly or 914%9 \frac { 1 } { 4 } \%941​% compounded annually?

Solve the problem. -What principal invested at 8% compounded continuously for 4 years will yield $1190? Round the answer to two decimal places.

Write the word or phrase that best completes each statement or answers the question. -What principal invested at 6%, compounded continuously for 3 years, will yield $1500? Round the answer to two decimal places.

Choose the one alternative that best completes the statement or answers the question. -How much money needs to be invested now to get $2000 after 4 years at 8% compounded quarterly? Express your answer to the nearest dollar.

Choose the one alternative that best completes the statement or answers the question. Find the effective rate of interest. -12% compounded continuously

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -A local bank advertises that it pays interest on savings accounts at the rate of 3% compounded monthly. Find the effective rate. Round answer to two decimal places.

Find the present value. Round to the nearest cent. -To get $10,000 after 3 years at 6% compounded monthly

Choose the one alternative that best completes the statement or answers the question. Find the effective rate of interest. -11.8% compounded continuously

Find the present value. Round to the nearest cent. -To get $2000 after 10 years at 9% compounded semiannually

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Which of the two rates would yield the larger amount in 1 year: 5.2% compounded monthly or 5.1% compounded daily?

Choose the one alternative that best completes the statement or answers the question. Find the effective rate of interest. -5.5% compounded quarterly

Find the present value. Round to the nearest cent. -To get $5600 after 8 years at 5% compounded annually

Find the present value. Round to the nearest cent. -To get $25,000 after 6 years at 10% compounded semiannually

Choose the one alternative that best completes the statement or answers the question. Find the effective rate of interest. - $6 \frac { 1 } { 4 } \%$ compounded monthly

Write the word or phrase that best completes each statement or answers the question. - $4 \frac { 3 } { 4 } \% \text { compounded quarterly }$

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Which of the two rates would yield the larger amount in 1 year: $9 \%$ compounded monthly or $9 \frac { 1 } { 4 } \%$ compounded annually?