Question 1

Find the effective annual interest rate for the given nominal annual interest rate. Round your answers to the nearest
0.01%.
-5% compounded semiannually

Accepted Answer

The answer of Find the effective annual interest rate for...

Question 2

Find the effective annual interest rate for the given nominal annual interest rate. Round your answers to the nearest
0.01%.
-4.1% compounded hourly (assume 365 days per year)

Accepted Answer

The effective annual interest rate can be calculated using the formula: $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount after time $t$, $P$ is the principal amount (initial investment), $r$ is the annual nominal interest rate (as a decimal), $n$ is the number of compounding periods per year, and $t$ is the time the money is invested for in years. To find the effective annual rate (EAR), we set $P = 1$ and $t = 1$, and solve for $A$, then calculate $EAR = (A - 1) \times 100\% $.Given: $r = 4.1\% = 0.041$, $n = 24 \times 365$ (since it's compounded hourly and there are 24 hours in a day), and $t = 1$ year.$A = (1 + \frac{0.041}{24 \times 365})^{24 \times 365}$Calculating this gives an $A$ value slightly greater than 1.0419, and converting this to a percentage and subtracting 100% gives an EAR slightly above 4.18%, which when rounded to the nearest 0.01% is 4.19%.

Question 3

Find the effective annual interest rate for the given nominal annual interest rate. Round your answers to the nearest
0.01%.
-3.9% compounded every minute (assume 365 days per year)

Accepted Answer

The effective annual interest rate can be calculated using the formula $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount after time $t$, $P$ is the principal amount, $r$ is the nominal annual interest rate, $n$ is the number of compounding periods per year, and $t$ is the time in years. For an interest rate of 3.9% compounded every minute, we have $r = 0.039$, $n = 365 \times 24 \times 60$, and $t = 1$. The effective annual interest rate is calculated as $(1 + \frac{0.039}{365 \times 24 \times 60})^{365 \times 24 \times 60} - 1$, which rounds to approximately 3.98%.

Question 4

Solve the problem.
-Joe is buying some kitchen equipment for his new apartment. The total cost is $3400 and he places a down payment of $340. There is add-on interest of 9%. What is the total amount to be repaid if he
Takes 5 years to pay for the purchase?

Accepted Answer

The principal amount after the down payment is $3400 - $340 = $3060. The interest is 9% of $3060, which is $275.40 per year. Over 5 years, the total interest is $275.40 * 5 = $1377. The total amount to be repaid is the principal plus the total interest: $3060 + $1377 = $4437.00.

Question 5

Solve the problem.
-You just put $1650 in a CD that is expected to earn 9% compounded quarterly, and $30,000 in a savings account that is expected to earn 4% compounded semiannually. Determine when, to the
Nearest year, the values of your two investments will be the same.

Accepted Answer

The answer of Solve the problem.
-You just put $1650 in...

Question 6

Solve the problem.
-Joe is buying some kitchen equipment for his new apartment. The total cost is $3700 and he places a down payment of $370. There is add-on interest of 9%. Find the total interest Joe will pay if it takes
Him 3 year(s)to pay for his purchase?

Accepted Answer

The principal amount after the down payment is $3700 - $370 = $3330. The interest is calculated as 9% of $3330 over 3 years, which is $3330 * 0.09 * 3 = $899.10.

Question 7

Solve the problem.
-The average cost of a 4-year college education is projected to be $120,000 in 15 years. How much money should be invested now at 7.5%, compounded quarterly, to provide $120,000 in 15 years?

Accepted Answer

To find the present value (the amount that should be invested now) to achieve a future value of $120,000 in 15 years at an interest rate of 7.5% compounded quarterly, we use the formula for the present value of a single sum: $PV = \frac{FV}{(1 + r/n)^{nt}}$, where PV is the present value, FV is the future value ($120,000), r is the annual interest rate (7.5% or 0.075), n is the number of times the interest is compounded per year (4 for quarterly), and t is the time in years (15). Plugging in the values, we get $PV = \frac{120,000}{(1 + 0.075/4)^{4*15}}$, which calculates to approximately $39,366.24.

Question 8

Solve the problem.
-Use the rule of 70 to estimate the annual inflation rate (to the nearest tenth of a percent)that would cause the general level of prices to double in 28 years.

Accepted Answer

The rule of 70 is a way to estimate the number of years it takes for a quantity to double given a constant annual growth rate. It states that dividing 70 by the number of years it takes for the quantity to double gives the annual growth rate. In this case, dividing 70 by 28 years gives 2.5%, which is the annual inflation rate needed for prices to double in that time frame.

Question 9

Find the present value for the given future amount. Round to the nearest cent.
-A = $4900, 8 years r = 8% compounded quarterly

Accepted Answer

The answer of Find the present value for the given...

Question 10

Solve the problem.
-You have money in an account at 4% interest, compounded monthly. To the nearest year, how long will it take for your money to double?

Accepted Answer

To find the time it takes for money to double with compound interest, you can use the Rule of 72, which is a simplified formula to estimate the number of years required to double the invested money at a given annual rate of interest. Divide 72 by the interest rate to get the approximate time in years. For a 4% interest rate, 72 / 4 = 18. Since the interest is compounded monthly, the actual time will be slightly less than 18 years, but the closest answer provided is 17 years.

Question 11

Solve the problem.
-The 2006 price of a certain type of car is $24,700. Estimate the price of the same car in the year 2020. Assume a constant annual inflation rate of 2.2%. Give a number of significant figures consistent
With the 2006 price given.

Accepted Answer

The price of the car in 2020 can be estimated using the formula for compound interest: $P = P_0(1 + r)^t$, where $P$ is the future value, $P_0$ is the initial value ($24,700), $r$ is the annual rate (2.2% or 0.022), and $t$ is the time in years (2020 - 2006 = 14 years). Plugging in the values: $P = 24700(1 + 0.022)^{14}$, which calculates to approximately $33,497.28, matching choice B.

Question 12

Solve the problem.
-$8791 is deposited into a savings account at 8% interest, compounded annually. To the nearest year, how long will it take for the account balance to reach $1,000,000?

Accepted Answer

To find the number of years it will take for the initial deposit to grow to $1,000,000, we can use the formula for compound interest: $A = P(1 + r)^t$, 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:$$t = \frac{\log(A/P)}{\log(1 + r)}$$Plugging in the values from the problem:$$A = 1,000,000, P = 8791, r = 0.08$$$$t = \frac{\log(1,000,000/8791)}{\log(1 + 0.08)}$$$$t = \frac{\log(113.74)}{\log(1.08)}$$$$t \approx 61.7$$Rounding to the nearest year, it will take approximately 62 years for the account balance to reach $1,000,000.

Question 13

Find the effective annual interest rate for the given nominal annual interest rate. Round your answers to the nearest
0.01%.
-3% compounded quarterly

Accepted Answer

The answer of Find the effective annual interest rate for...

Question 14

Solve the problem.
-Use the rule of 70 to estimate the years to double for an annual inflation rate of 6%.

Accepted Answer

The rule of 70 is a way to estimate the number of years it will take for a quantity to double, given a fixed annual percentage increase. To use it, you divide 70 by the annual percentage increase. In this case, 70 divided by 6 equals approximately 11.67, which rounds to 12 years.

Question 15

Solve the problem.
-Joe is buying some kitchen equipment for his new apartment. The total cost is $2300 and he places a down payment of $230. There is add-on interest of 12%. What is the total amount he will be
Financing?

Accepted Answer

The total amount Joe is financing is the total cost minus the down payment, which is $2300 - $230 = $2070. The interest is not added to the financing amount at this stage.

Question 16

Find the effective annual interest rate for the given nominal annual interest rate. Round your answers to the nearest
0.01%.
-4.7% compounded monthly

Accepted Answer

The effective annual interest rate can be calculated using the formula: $ (1 + \frac{r}{n})^n - 1 $, where $ r $ is the nominal annual interest rate (expressed as a decimal) and $ n $ is the number of compounding periods per year. For a 4.7% interest rate compounded monthly, $ r = 0.047 $ and $ n = 12 $. Plugging these values into the formula gives an effective annual rate of approximately 4.80%.

Question 17

Solve the problem.
-Use the inflation proportion to estimate the 2005 price of a jacket which costs $470 in 2000. Assume that the price increased at the average annual rate shown in the table below. Round your answer to
The nearest dollar. $\begin{array}{l|c|c}
\text { Year } & \text { Average CPI-U } & \text { Percent Change in CPI-U } \
\hline 1999 & 166.6 & 2.2 \
2000 & 172.2 & 3.4 \
2001 & 177.1 & 2.8 \
2002 & 179.9 & 1.6 \
2003 & 184.0 & 2.3 \
2004 & 188.9 & 2.7 \
2005 & 195.3 & 3.4
\end{array}$

Accepted Answer

The answer of Solve the problem.
-Use the inflation proportion to...

Question 18

Solve the problem.
-Ellen invests her money in a savings account which compounds interest quarterly and which gives an effective annual yield of 4.18%. What is the nominal rate?

Accepted Answer

The nominal rate can be found using the formula for the effective annual rate (EAR) for interest compounded quarterly: $EAR = (1 + \frac{i}{4})^4 - 1$, where $i$ is the nominal rate divided by 100. Rearranging to solve for $i$, given an EAR of 4.18% or 0.0418, we get $i = 4 \times (\sqrt[4]{1 + 0.0418} - 1)$, which calculates to approximately 4.12%.

Question 19

Solve the problem.
-Miguel invests his money in a savings account which gives an effective annual yield of 3.5%. The nominal rate is 3.45%. How often does compounding occur - daily, monthly, quarterly, or
Semiannually?

Accepted Answer

The effective annual yield is 3.5% and the nominal rate is 3.45%. The difference between the two rates is 0.05%. This means that the compounding occurs quarterly, since 0.05% is equal to 1/24 of 1%.

Question 20

Find the effective annual interest rate for the given nominal annual interest rate. Round your answers to the nearest
0.01%.
-4.3% compounded daily (assume 365 days per year)

Accepted Answer

The effective annual interest rate (EAR) can be calculated using the formula EAR = (1 + r/n)^(n*t) - 1, where r is the nominal annual interest rate (expressed as a decimal), n is the number of compounding periods per year, and t is the time in years. For a 4.3% nominal rate compounded daily, EAR = (1 + 0.043/365)^(365*1) - 1 ≈ 0.0439 or 4.39%.

Quiz 13: Personal Financial Management

Find the effective annual interest rate for the given nominal annual interest rate. Round your answers to the nearest 0.01%. -5% compounded semiannually

Find the effective annual interest rate for the given nominal annual interest rate. Round your answers to the nearest 0.01%. -4.1% compounded hourly (assume 365 days per year)

Find the effective annual interest rate for the given nominal annual interest rate. Round your answers to the nearest 0.01%. -3.9% compounded every minute (assume 365 days per year)

Solve the problem. -Joe is buying some kitchen equipment for his new apartment. The total cost is $3400 and he places a down payment of $340. There is add-on interest of 9%. What is the total amount to be repaid if he Takes 5 years to pay for the purchase?

Solve the problem. -You just put $1650 in a CD that is expected to earn 9% compounded quarterly, and $30,000 in a savings account that is expected to earn 4% compounded semiannually. Determine when, to the Nearest year, the values of your two investments will be the same.

Solve the problem. -Joe is buying some kitchen equipment for his new apartment. The total cost is $3700 and he places a down payment of $370. There is add-on interest of 9%. Find the total interest Joe will pay if it takes Him 3 year(s) to pay for his purchase?

Solve the problem. -The average cost of a 4-year college education is projected to be $120,000 in 15 years. How much money should be invested now at 7.5%, compounded quarterly, to provide $120,000 in 15 years?

Solve the problem. -Use the rule of 70 to estimate the annual inflation rate (to the nearest tenth of a percent) that would cause the general level of prices to double in 28 years.

Find the present value for the given future amount. Round to the nearest cent. -A = $4900, 8 years r = 8% compounded quarterly

Solve the problem. -You have money in an account at 4% interest, compounded monthly. To the nearest year, how long will it take for your money to double?

Solve the problem. -The 2006 price of a certain type of car is $24,700. Estimate the price of the same car in the year 2020. Assume a constant annual inflation rate of 2.2%. Give a number of significant figures consistent With the 2006 price given.

Solve the problem. -$8791 is deposited into a savings account at 8% interest, compounded annually. To the nearest year, how long will it take for the account balance to reach $1,000,000?

Find the effective annual interest rate for the given nominal annual interest rate. Round your answers to the nearest 0.01%. -3% compounded quarterly

Solve the problem. -Use the rule of 70 to estimate the years to double for an annual inflation rate of 6%.

Solve the problem. -Joe is buying some kitchen equipment for his new apartment. The total cost is $2300 and he places a down payment of $230. There is add-on interest of 12%. What is the total amount he will be Financing?

Find the effective annual interest rate for the given nominal annual interest rate. Round your answers to the nearest 0.01%. -4.7% compounded monthly

Solve the problem. -Ellen invests her money in a savings account which compounds interest quarterly and which gives an effective annual yield of 4.18%. What is the nominal rate?

Solve the problem. -Miguel invests his money in a savings account which gives an effective annual yield of 3.5%. The nominal rate is 3.45%. How often does compounding occur - daily, monthly, quarterly, or Semiannually?

Find the effective annual interest rate for the given nominal annual interest rate. Round your answers to the nearest 0.01%. -4.3% compounded daily (assume 365 days per year)