Question 1

Calculate the future value of an investment of $14,000 at 5.5% per year, compounded weekly, after 6 years. Assume 52 weeks per year. ​

Accepted Answer

The answer of Calculate the future value of an investment...

Question 2

Calculate, to the nearest 0.1%, what annual interest rate would be required if you invested $6,000 in Apple stock and ended up with $15,622 when you sold the stock after 5 years  Assume that interest was compounded quarterly. ?

Accepted Answer

Using the formula for compound interest with quarterly compounding, we have:

$15,622 = $6,000 (1 + r/4)^(4*5)
2.6037 = (1 + r/4)^20
Taking the 20th root of both sides:
1.1148 = 1 + r/4
r/4 = 0.1148
r = 0.4592 or 45.92%

However, we need to convert this to an annual interest rate. Since interest is compounded quarterly, we need to use the formula:

A = P(1 + r/n)^(nt)

where A is the ending amount, P is the principal, r is the annual interest rate, n is the number of times compounded per year, and t is the number of years. Solving for r, we have:

r = n[(A/P)^(1/nt) - 1]

Plugging in the values we know, we get:

r = 4[(15622/6000)^(1/20) - 1] ≈ 0.194 or 19.4%

Therefore, the answer is choice B, 19.6%, which is the closest to our calculated value of 19.4%.

Question 3

Calculate, to the nearest cent, the present value of an investment that will be worth $16,000 after 7 years, at 7.4% compounded quarterly.

Accepted Answer

The answer of Calculate, to the nearest cent, the present...

Question 4

Calculate the future value of an investment of $3,500, after one year, if it is deposited in a savings account that is compounded quarterly at an annual rate of 11%. Round your answer to the nearest cent. ​

Accepted Answer

The future value is calculated using the formula for compound interest: FV = P(1 + r/n)^(nt), where P = $3,500, r = 0.11, n = 4, and t = 1. Plugging in these values gives FV = $3,500(1 + 0.11/4)^(4*1) = $3,901.17.

Question 5

You are offered three investments. What is the best investment  ?

Accepted Answer

The second option, with a 19.5% interest rate compounded quarterly, offers the best investment due to the effect of more frequent compounding periods within a year, which results in a higher effective annual rate compared to the other options.

Question 6

Calculate, to the nearest cent, the present value of an investment that will be worth $4,000 after 9 years, at 10% per year, compounded annually.

Accepted Answer

The present value $PV$ of an investment can be calculated using the formula $PV = \frac{FV}{(1 + r)^n}$, where $FV$ is the future value, $r$ is the annual interest rate (as a decimal), and $n$ is the number of years. Plugging in the given values: $PV = \frac{4000}{(1 + 0.10)^9} = \$1,696.39$.

Question 7

Inflation has been running 6% per year. A car now costs $32,000. How much would it have cost 9 years ago

Accepted Answer

The correct answer is D.The formula for calculating the cost of a car 9 years ago is:Cost 9 years ago = Cost now / (1 + inflation rate)^number of yearsCost 9 years ago = $32,000 / (1 + 0.06)^9Cost 9 years ago = $18,940.75

Question 8

How much would you have to invest when you are 20 years old at 9% compounded monthly to end up with a million dollars by age 48  Round your answer to the nearest thousand. ?

Accepted Answer

The answer of How much would you have to invest...

Question 9

Find the effective annual interest rate of 17% compounded monthly. ​

Accepted Answer

We can use the formula for effective annual interest rate:

Effective annual rate = (1 + (nominal rate / m))^m - 1

where nominal rate is the stated annual interest rate and m is the number of compounding periods in a year.

In this case, nominal rate = 17% and m = 12 (since it's compounded monthly).

Plugging in the values, we get:

Effective annual rate = (1 + (0.17 / 12))^12 - 1 ≈ 0.1839 or 18.39%

Therefore, the answer is B.

Question 10

Calculate the future value of an investment of $5,000 at 0.8% per year, compounded monthly, after 8 years. Round your answer to the nearest cent. ​

Accepted Answer

The future value of an investment can be calculated using the formula FV = P(1 + r/n)^(nt), where P is the principal amount ($5,000), r is the annual interest rate (0.8% or 0.008), n is the number of times the interest is compounded per year (12 for monthly), and t is the time the money is invested for (8 years). Plugging in the values, FV = $5,000(1 + 0.008/12)^(12*8) ≈ $5,330.35.

Question 11

Determine the amount of money, to the nearest dollar, you must invest now at 5% per year compounded annually, so that you will be a millionaire in 50 years.

Accepted Answer

The answer of Determine the amount of money, to the...

Question 12

$10,000 is deposited in a money market account when interest is compounded every month at an annual rate of 6%. Find the total amount accumulated at the end of 5 years. Round your answer to the nearest cent. ​

Accepted Answer

The formula for compound interest is:

A = P(1 + r/n)^(nt)

Where:

A = the total amount accumulated 
P = the principal amount 
r = the annual interest rate (as a decimal) 
n = the number of times the interest is compounded per year 
t = the time period in years

Using this formula, the total amount accumulated after 5 years is:

A = 10000(1 + 0.06/12)^(12*5) 
A = 10000(1.005)^60 
A = $13,488.50

Therefore, the best choice is C.

Question 13

Calculate the present value of an investment that will be worth $2,000 after 3 years at 8% per year compounded annually. Round your answer to the nearest cent. ​

Accepted Answer

We can use the formula PV = FV/(1+r)^n where PV is the present value, FV is the future value, r is the annual interest rate and n is the number of years. Substituting the given values, we get PV = 2000/(1+0.08)^3 = $1,587.66. Therefore, the best choice is A.

Question 14

You invest $13,000 in Rapid Growth Funds, which appreciate by 2% per year, with yields reinvested quarterly. By how much will your investment have grown after 7 years  Round your answer to the nearest cent. ?

Accepted Answer

The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, 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. Given that $P = \$13,000$, $r = 0.02$ (2% annual interest rate), $n = 4$ (compounded quarterly), and $t = 7$ years, we calculate $A$ as follows:$$A = 13000(1 + \frac{0.02}{4})^{4*7}$$$$A = 13000(1 + 0.005)^{28}$$$$A = 13000(1.005)^{28}$$$$A ≈ 13000 * 1.149562$$$$A ≈ \$14943.31$$Since none of the provided options match this calculation, the correct answer is E) None of these.

Question 15

Find the effective annual interest rate of 4% compounded quarterly. ​

Accepted Answer

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

Question 16

The effective rate exceeds the nominal rate when the interest is compounded more than once a year resulting in a larger effective rate.

Accepted Answer

This statement is true. When interest is compounded more than once a year, the effective rate takes into account the compounding of interest, resulting in a higher effective rate than the nominal rate.

Question 17

Calculate, to the nearest cent, the future value of an investment of $28,000 at 10.45% per year, compounded monthly, after 14 years.

Accepted Answer

The future value $FV$ of an investment is calculated using the formula $FV = P(1 + \frac{r}{n})^{nt}$, where $P$ is the principal amount (\$28,000), $r$ is the annual interest rate (10.45% or 0.1045), $n$ is the number of times the interest is compounded per year (12, since it's compounded monthly), and $t$ is the time the money is invested for (14 years). Plugging these values into the formula gives $FV = 28000(1 + \frac{0.1045}{12})^{12*14}$, which calculates to approximately \$120,165.64.

Question 18

Find the effective annual interest rate of 11% compounded monthly. Round your answer to the nearest 0.01%.

Accepted Answer

The effective annual interest rate is given by the formula:$r _ { \text {eff } } = (1 + \frac { r } { n } ) ^ { n } - 1$where:$r$ is the nominal annual interest rate$n$ is the number of compounding periods per yearIn this case, the nominal annual interest rate is 11% and the number of compounding periods per year is 12 (since the interest is compounded monthly). Plugging these values into the formula, we get:$r _ { \text {eff } } = (1 + \frac { 0.11 } { 12 } ) ^ { 12 } - 1 = 0.1157$Rounding this to the nearest 0.01%, we get 11.57%.

Question 19

Calculate, to the nearest cent, the future value of an investment of $14,000 at 4.25% per year, compounded quarterly (4 times per year), after 7 years.

Accepted Answer

The future value $FV$ of an investment is calculated using the formula $FV = P(1 + \frac{r}{n})^{nt}$, where $P$ is the principal amount ($14,000), $r$ is the annual interest rate (4.25% or 0.0425), $n$ is the number of times the interest is compounded per year (4), and $t$ is the time the money is invested for (7 years). Plugging these values into the formula gives $FV = 14000(1 + \frac{0.0425}{4})^{4*7}$, which calculates to approximately $18,821.28.

Question 20

Doubling the frequency of compounding in a compound interest investment will not double the amount of the interest.

Accepted Answer

Doubling the frequency of compounding increases the amount of interest, but due to the exponential nature of compound interest, it does not double the amount of interest earned. The increase is due to more frequent application of the interest rate, but the effect is not linear.

Quiz 3: The Mathematics of Finance

Calculate the future value of an investment of $14,000 at 5.5% per year, compounded weekly, after 6 years. Assume 52 weeks per year.

Calculate, to the nearest 0.1%, what annual interest rate would be required if you invested $6,000 in Apple stock and ended up with $15,622 when you sold the stock after 5 years Assume that interest was compounded quarterly. ?

Calculate, to the nearest cent, the present value of an investment that will be worth $16,000 after 7 years, at 7.4% compounded quarterly.

Calculate the future value of an investment of $3,500, after one year, if it is deposited in a savings account that is compounded quarterly at an annual rate of 11%. Round your answer to the nearest cent.

You are offered three investments. What is the best investment ?

Calculate, to the nearest cent, the present value of an investment that will be worth $4,000 after 9 years, at 10% per year, compounded annually.

Inflation has been running 6% per year. A car now costs $32,000. How much would it have cost 9 years ago

How much would you have to invest when you are 20 years old at 9% compounded monthly to end up with a million dollars by age 48 Round your answer to the nearest thousand. ?

Find the effective annual interest rate of 17% compounded monthly.

Calculate the future value of an investment of $5,000 at 0.8% per year, compounded monthly, after 8 years. Round your answer to the nearest cent.

Determine the amount of money, to the nearest dollar, you must invest now at 5% per year compounded annually, so that you will be a millionaire in 50 years.

$10,000 is deposited in a money market account when interest is compounded every month at an annual rate of 6%. Find the total amount accumulated at the end of 5 years. Round your answer to the nearest cent.

Calculate the present value of an investment that will be worth $2,000 after 3 years at 8% per year compounded annually. Round your answer to the nearest cent.

You invest $13,000 in Rapid Growth Funds, which appreciate by 2% per year, with yields reinvested quarterly. By how much will your investment have grown after 7 years Round your answer to the nearest cent. ?

Find the effective annual interest rate of 4% compounded quarterly.

The effective rate exceeds the nominal rate when the interest is compounded more than once a year resulting in a larger effective rate.

Calculate, to the nearest cent, the future value of an investment of $28,000 at 10.45% per year, compounded monthly, after 14 years.

Find the effective annual interest rate of 11% compounded monthly. Round your answer to the nearest 0.01%.

Calculate, to the nearest cent, the future value of an investment of $14,000 at 4.25% per year, compounded quarterly (4 times per year) , after 7 years.

Doubling the frequency of compounding in a compound interest investment will not double the amount of the interest.

Quiz 3: The Mathematics of Finance

Calculate the future value of an investment of $14,000 at 5.5% per year, compounded weekly, after 6 years. Assume 52 weeks per year. ​

Calculate, to the nearest 0.1%, what annual interest rate would be required if you invested $6,000 in Apple stock and ended up with $15,622 when you sold the stock after 5 years Assume that interest was compounded quarterly. ?

Calculate, to the nearest cent, the present value of an investment that will be worth $16,000 after 7 years, at 7.4% compounded quarterly.

Calculate the future value of an investment of $3,500, after one year, if it is deposited in a savings account that is compounded quarterly at an annual rate of 11%. Round your answer to the nearest cent. ​

You are offered three investments. What is the best investment ?

Calculate, to the nearest cent, the present value of an investment that will be worth $4,000 after 9 years, at 10% per year, compounded annually.

Inflation has been running 6% per year. A car now costs $32,000. How much would it have cost 9 years ago

How much would you have to invest when you are 20 years old at 9% compounded monthly to end up with a million dollars by age 48 Round your answer to the nearest thousand. ?

Find the effective annual interest rate of 17% compounded monthly. ​

Calculate the future value of an investment of $5,000 at 0.8% per year, compounded monthly, after 8 years. Round your answer to the nearest cent. ​

Determine the amount of money, to the nearest dollar, you must invest now at 5% per year compounded annually, so that you will be a millionaire in 50 years.

$10,000 is deposited in a money market account when interest is compounded every month at an annual rate of 6%. Find the total amount accumulated at the end of 5 years. Round your answer to the nearest cent. ​

Calculate the present value of an investment that will be worth $2,000 after 3 years at 8% per year compounded annually. Round your answer to the nearest cent. ​

You invest $13,000 in Rapid Growth Funds, which appreciate by 2% per year, with yields reinvested quarterly. By how much will your investment have grown after 7 years Round your answer to the nearest cent. ?

Find the effective annual interest rate of 4% compounded quarterly. ​

The effective rate exceeds the nominal rate when the interest is compounded more than once a year resulting in a larger effective rate.

Calculate, to the nearest cent, the future value of an investment of $28,000 at 10.45% per year, compounded monthly, after 14 years.

Find the effective annual interest rate of 11% compounded monthly. Round your answer to the nearest 0.01%.

Calculate, to the nearest cent, the future value of an investment of $14,000 at 4.25% per year, compounded quarterly (4 times per year) , after 7 years.

Doubling the frequency of compounding in a compound interest investment will not double the amount of the interest.

Calculate the future value of an investment of $14,000 at 5.5% per year, compounded weekly, after 6 years. Assume 52 weeks per year.

Calculate the future value of an investment of $3,500, after one year, if it is deposited in a savings account that is compounded quarterly at an annual rate of 11%. Round your answer to the nearest cent.

Find the effective annual interest rate of 17% compounded monthly.

Calculate the future value of an investment of $5,000 at 0.8% per year, compounded monthly, after 8 years. Round your answer to the nearest cent.

$10,000 is deposited in a money market account when interest is compounded every month at an annual rate of 6%. Find the total amount accumulated at the end of 5 years. Round your answer to the nearest cent.

Calculate the present value of an investment that will be worth $2,000 after 3 years at 8% per year compounded annually. Round your answer to the nearest cent.

Find the effective annual interest rate of 4% compounded quarterly.