Question 1

Solve the problem.
-Find the future value accumulated in an annuity after investing periodic payments of $134 for 8 years at an annual interest rate of 5%, with payments made and credited 4 times per year.

Accepted Answer

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-Find the future value accumulated...

Question 2

Solve the problem.
-How long will it take for $5100 to grow to $5300 at an interest rate of 4.4% if the interest is compounded continuously? Round the number of years to the nearest hundredth.

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 (the initial amount of money), $r$ is the annual interest rate (decimal), and $t$ is the time the money is invested for in years. Rearranging the formula to solve for $t$, we get $t = \frac{\ln(A/P)}{r}$. Plugging in the given values: $A = 5300$, $P = 5100$, and $r = 0.044$, we get $t = \frac{\ln(5300/5100)}{0.044}$, which approximately equals 0.87 years.

Question 3

Solve the problem.
-Find the present value of a loan with an annual interest rate of 6.7% and periodic payments of $1266.21 for a term of 30 years, with payments made and interest charged 12 times per year.

Accepted Answer

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-Find the present value of...

Question 4

Solve the problem.
-Find the interest rate necessary for a present value of $18,401 to grow to a future value of $21,559.70 if interest is compounded quarterly for two years.

Accepted Answer

The formula for compound interest is $ FV = PV \times (1 + \frac{r}{n})^{nt} $. Plugging in the values: $ 21,559.70 = 18,401 \times (1 + \frac{r}{4})^{8} $. Solving for $ r $ gives approximately 8%.

Question 5

Determine the doubling time of the investment.
-6% APR compounded annually

Accepted Answer

The Rule of 72 estimates the doubling time by dividing 72 by the annual interest rate. For 6% APR, 72/6 = 12 years, which is closest to 11.9 years.

Question 6

Solve the problem.
-Assume the cost of a gallon of milk is $2.50. With continuous compounding, find the time it would take the cost to be 2 times as much (to the nearest tenth of a year), at an annual inflation rate of 6%.

Accepted Answer

The formula for continuous compounding is $A = Pe^{rt}$, where $A$ is the amount after time $t$, $P$ is the principal amount, $r$ is the rate, and $e$ is the base of the natural logarithm. Here, we want the amount $A$ to be twice the principal $P$, so $2P = Pe^{0.06t}$. Dividing both sides by $P$ and taking the natural logarithm of both sides gives $\ln(2) = 0.06t$. Solving for $t$ gives $t = \frac{\ln(2)}{0.06} \approx 11.6$ years.

Question 7

Determine the doubling time of the investment.
-$1100 at 7% compounded quarterly

Accepted Answer

The answer of Determine the doubling time of the investment.
-$1100...

Question 8

Solve the problem.
-At what interest rate must $5100 be compounded annually to equal $8189.49 after 7 yr? (Round to the nearest percent.)

Accepted Answer

The answer of Solve the problem.
-At what interest rate must...

Question 9

Solve the problem.
-Find the periodic payment of a loan with present value $20,000 and an annual interest rate 6.3% for a term of 3 years, with payments made and interest charged 12 times per year.

Accepted Answer

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-Find the periodic payment of...

Question 10

Solve the problem.
-Find how long it will take for $8600 invested at 9.325% per year compounded daily to triple in value. Find the answer to the nearest year.

Accepted Answer

To find the time it takes for an investment to triple in value with daily compounding interest, we use the formula $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years. To triple the investment, $A = 3P$. Given $P = \$8600$, $r = 9.325\% = 0.09325$, and $n = 365$ (since the interest is compounded daily), we solve for $t$:$$3P = P(1 + \frac{0.09325}{365})^{365t}$$$$3 = (1 + \frac{0.09325}{365})^{365t}$$Taking the natural logarithm of both sides:$$\ln(3) = 365t \ln(1 + \frac{0.09325}{365})$$$$t = \frac{\ln(3)}{365 \ln(1 + \frac{0.09325}{365})}$$Calculating this gives a value close to 12 years, hence the investment will take approximately 12 years to triple in value.

Question 11

Solve the problem.
-How long will it take for prices in the economy to double at a 9% annual inflation rate? (Round to the nearest year.)

Accepted Answer

The Rule of 72 is a simple way to estimate the number of years required to double the investment at a given annual rate of return. By dividing 72 by the annual rate of return, investors can get a rough estimate of how many years it will take for the initial investment to duplicate itself. In this case, dividing 72 by the annual inflation rate of 9% gives 8 years (72 / 9 = 8).

Question 12

Solve the problem.
-How long must $4100 be in a bank at 8% compounded annually to become $10,324.50? (Round to the nearest year.)

Accepted Answer

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times per year that the interest is compounded, and t is the number of years.In this case, we have A = $10,324.50, P = $4100, r = 8%, n = 1 (compounded annually), and we want to find t.Substituting these values into the formula, we get:10324.50 = 4100(1 + 0.08/1)^(1*t)10324.50 = 4100(1.08)^t10324.50/4100 = 1.08^t2.51817 = 1.08^tt = log(2.51817)/log(1.08)t = 12.00Therefore, the answer is C) 12 yr.

Question 13

Solve the problem.
-Find the periodic payment of a loan with present value $1500 and an annual interest rate 8.9% for a term of 3 years, with payments made and interest charged 12 times per year.

Accepted Answer

The periodic payment can be calculated using the formula for an ordinary annuity: PMT = P * (r(1+r)^n) / ((1+r)^n - 1), where P is the present value, r is the monthly interest rate, and n is the total number of payments. Here, P = $1500, the annual interest rate is 8.9%, so the monthly rate r = 0.089/12, and n = 3*12. Plugging these values into the formula gives the periodic payment of approximately $47.63.

Question 14

Solve the problem.
-How long will it take for $1100 to grow to $4800 at an interest rate of 10.9% if the interest is compounded quarterly? Round the number of years to the nearest hundredth.

Accepted Answer

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-How long will it take...

Question 15

Solve the problem.
-Find the present value of a loan with an annual interest rate of 5.9% and periodic payments of $778.63 for a term of 7 years, with payments made and interest charged 12 times per year.

Accepted Answer

The present value $PV$ of an annuity (in this case, a loan payment) can be calculated using the formula: $$PV = P \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)$$ where $P$ is the periodic payment amount, $r$ is the periodic interest rate (annual rate divided by the number of periods per year), and $n$ is the total number of payments (years times the number of periods per year).Given:- Annual interest rate = 5.9% or 0.059 when expressed as a decimal.- Periodic payments = $778.63.- Term = 7 years.- Payments made and interest charged 12 times per year.First, calculate the periodic interest rate:$$r = \frac{0.059}{12}$$Then, calculate the total number of payments:$$n = 7 \times 12$$Substitute these values into the formula:$$PV = 778.63 \times \left(\frac{1 - (1 + \frac{0.059}{12})^{-7 \times 12}}{\frac{0.059}{12}}\right)$$This calculation will give you the present value of the loan, which is approximately $53,474.90, matching choice B.

Question 16

Determine the doubling time of the investment.
-$14,500 at 6% compounded monthly

Accepted Answer

The doubling time can be calculated using the Rule of 72, which is an approximation. For a 6% interest rate compounded monthly, the effective annual rate is slightly higher than 6%. However, using the Rule of 72, 72 divided by 6 gives approximately 12 years. More precise calculations using the formula for compound interest confirm that the doubling time is approximately 11.58 years.

Question 17

Solve the problem.
-Find the periodic payment of a loan with present value $161,000 and an annual interest rate 5% for a term of 24 years, with payments made and interest charged 12 times per year.

Accepted Answer

The periodic payment can be calculated using the formula for the payment of an annuity: $PMT = \frac{PV \times r}{1 - (1 + r)^{-n}}$, where $PMT$ is the periodic payment, $PV$ is the present value of the loan, $r$ is the monthly interest rate (annual rate divided by 12), and $n$ is the total number of payments (years times 12). Here, $PV = 161,000$, $r = 0.05/12$, and $n = 24 \times 12$. Plugging these values into the formula gives $PMT = \frac{161,000 \times (0.05/12)}{1 - (1 + 0.05/12)^{-288}} \approx 961.00$.

Question 18

Solve the problem.
-Find the future value accumulated in an annuity after investing periodic payments of $20 for 19 years at an annual interest rate of 7%, with payments made and credited 12 times per year.

Accepted Answer

The answer of Solve the problem.
-Find the future value accumulated...

Question 19

Determine the doubling time of the investment.
-8% APR compounded continuously

Accepted Answer

The doubling time for continuous compounding is given by the formula t = (ln 2) / r, where r is the annual interest rate. In this case, r = 0.08, so t = (ln 2) / 0.08 = 8.66 years.

Question 20

Solve the problem.
-Find the present value of a loan with an annual interest rate of 6.7% and periodic payments of $288.46 for a term of 3 years, with payments made and interest charged 12 times per year.

Accepted Answer

The answer of Solve the problem.
-Find the present value of...

Quiz 3: Exponential, Logistic, and Logarithmic Functions

Solve the problem. -Find the future value accumulated in an annuity after investing periodic payments of $134 for 8 years at an annual interest rate of 5%, with payments made and credited 4 times per year.

Solve the problem. -How long will it take for $5100 to grow to $5300 at an interest rate of 4.4% if the interest is compounded continuously? Round the number of years to the nearest hundredth.

Solve the problem. -Find the present value of a loan with an annual interest rate of 6.7% and periodic payments of $1266.21 for a term of 30 years, with payments made and interest charged 12 times per year.

Solve the problem. -Find the interest rate necessary for a present value of $18,401 to grow to a future value of $21,559.70 if interest is compounded quarterly for two years.

Determine the doubling time of the investment. -6% APR compounded annually

Solve the problem. -Assume the cost of a gallon of milk is $2.50. With continuous compounding, find the time it would take the cost to be 2 times as much (to the nearest tenth of a year) , at an annual inflation rate of 6%.

Determine the doubling time of the investment. -$1100 at 7% compounded quarterly

Solve the problem. -At what interest rate must $5100 be compounded annually to equal $8189.49 after 7 yr? (Round to the nearest percent.)

Solve the problem. -Find the periodic payment of a loan with present value $20,000 and an annual interest rate 6.3% for a term of 3 years, with payments made and interest charged 12 times per year.

Solve the problem. -Find how long it will take for $8600 invested at 9.325% per year compounded daily to triple in value. Find the answer to the nearest year.

Solve the problem. -How long will it take for prices in the economy to double at a 9% annual inflation rate? (Round to the nearest year.)

Solve the problem. -How long must $4100 be in a bank at 8% compounded annually to become $10,324.50? (Round to the nearest year.)

Solve the problem. -Find the periodic payment of a loan with present value $1500 and an annual interest rate 8.9% for a term of 3 years, with payments made and interest charged 12 times per year.

Solve the problem. -How long will it take for $1100 to grow to $4800 at an interest rate of 10.9% if the interest is compounded quarterly? Round the number of years to the nearest hundredth.

Solve the problem. -Find the present value of a loan with an annual interest rate of 5.9% and periodic payments of $778.63 for a term of 7 years, with payments made and interest charged 12 times per year.

Determine the doubling time of the investment. -$14,500 at 6% compounded monthly

Solve the problem. -Find the periodic payment of a loan with present value $161,000 and an annual interest rate 5% for a term of 24 years, with payments made and interest charged 12 times per year.

Solve the problem. -Find the future value accumulated in an annuity after investing periodic payments of $20 for 19 years at an annual interest rate of 7%, with payments made and credited 12 times per year.

Determine the doubling time of the investment. -8% APR compounded continuously

Solve the problem. -Find the present value of a loan with an annual interest rate of 6.7% and periodic payments of $288.46 for a term of 3 years, with payments made and interest charged 12 times per year.