Question 1

If you deposit $1,000 in an account that earns 5% per year (compounded monthly),what will the balance in the account be at the end of 5 years?

Accepted Answer

The balance in the account at the end of 5 years can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount ($1,000), r is the annual interest rate (5% or 0.05), n is the number of times that interest is compounded per year (12), and t is the time the money is invested for in years (5). Plugging in the values: A = 1000(1 + 0.05/12)^(12*5) = $1,283.36. Rounding to the nearest dollar gives $1,283.

Question 2

Assuming an interest rate of 6%,the present value of $1 that will be received a year from now is $0.75.

Accepted Answer

$0.94

Question 3

The future value compound factor given for period (n)at 15%:

Accepted Answer

As the interest rate is constant at 15%, the future value compound factor will increase as the time period (n) increases. Therefore, the factor for period (n + 1) will be greater than the factor for period (n) at 15%.

Question 4

The future value of a single deposit of $1,000 will be greatest when this amount is compounded:

Accepted Answer

The future value of a deposit will be greatest when it is compounded more frequently. The more frequent the compounding, the more interest will be earned on the original deposit. Out of the options given, monthly compounding (choice D) is the most frequent and will result in the highest future value for the $1,000 deposit.

Question 5

Ten years ago,you put $150,000 into an interest-earning account.Today it is worth $275,000.What is the effective annual interest earned on the account?

Accepted Answer

The effective annual interest rate can be calculated using the formula for compound interest: $A = P(1 + r)^n$, 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 $n$ is the time the money is invested for in years. Rearranging the formula to solve for $r$, we get $r = \left(\frac{A}{P}\right)^{\frac{1}{n}} - 1$. Substituting the given values ($A = 275,000$, $P = 150,000$, and $n = 10$) into the formula gives $r = \left(\frac{275,000}{150,000}\right)^{\frac{1}{10}} - 1 \approx 0.0625$ or 6.25%.

Question 6

Assume that an investment,with a single initial cost of $1,000 and a yield of $50 monthly for 10 years,had a 7% IRR in the 60th month and a 7.2% IRR five months later.The IRR can be 6.8% in the 62nd month.

Accepted Answer

IRR (Internal Rate of Return) is a metric used to evaluate the profitability of potential investments. It is a constant value for a given set of cash flows (an initial investment followed by a series of returns). The IRR does not fluctuate from month to month; it is determined by the initial investment and the pattern of returns. The scenario described suggests a misunderstanding of how IRR works; it would not change in the manner described if the cash flows remain as initially defined.

Question 7

The future value of $800 deposited today would be greater if that deposit earned 8% rather than 7.75%.

Accepted Answer

The higher the interest rate, the more quickly the money will grow, resulting in a higher future value. Therefore, if the deposit earned 8% instead of 7.75%, the future value would be greater.

Question 8

Your friend just won the lottery.He has a choice of receiving $50,000 a year for the next 20 years or a lump sum today.The lottery uses a 15% discount rate.What would be the lump sum amount your friend would receive?

Accepted Answer

The lump sum amount can be calculated using the present value formula for an annuity: PV = P * [(1 - (1 + r)^-n) / r], where P is the payment amount ($50,000), r is the discount rate (15% or 0.15), and n is the number of periods (20 years). Plugging in the values: PV = $50,000 * [(1 - (1 + 0.15)^-20) / 0.15] ≈ $312,967.

Question 9

The future value of a $1 annuity compounded at 5% annually is greater than the future value of a $1 annuity compounded at 5% semi-annually.

Accepted Answer

The future value of an annuity compounded more frequently (semi-annually in this case) will be greater than one compounded less frequently (annually) due to the effects of compounding interest more often.

Question 10

Your friend has a trust fund that will pay him $100,000 at the end of 10 years.Your friend,however,wants his money today.He promises to sign his trust fund over to you if you give him some money today.You require a 20% interest rate on money you lend to friends.How much would you be willing to lend under these terms?

Accepted Answer

To calculate the present value of the trust fund payment, we can use the formula:
Present value = Future value / (1 + interest rate)^n
Where n is the number of years until the payment is received.
Plugging in the values, we get:
Present value = 100,000 / (1 + 0.2)^10
Present value = $16,151. Therefore, you would be willing to lend up to $16,151 to your friend under these terms.

Question 11

An investment may have more than one internal rate of return.

Accepted Answer

An investment may have more than one internal rate of return if it involves non-conventional cash flows (i.e. there are multiple changes in the sign of the cash flows). In such cases, the investment may have multiple IRRs or even none.

Question 12

Begin with a single sum of money at period 0.First,calculate a future value of that sum at 12.01%.Then discount that future value back to period 0 at 11.99%.In relation to the initial single sum,the discounted future value:

Accepted Answer

The future value at 12.01% is higher than the original amount because of the interest earned. When this future value is discounted back to period 0 at a slightly lower rate of 11.99%, the value should still be higher than the original amount, although not by as much as it would have been if the discount rate were the same as the interest rate. Therefore, the discounted future value is greater than the original amount.

Question 13

The internal rate of return is the good feeling you get inside when you earn a return on your investment.

Accepted Answer

The internal rate of return (IRR) is actually a financial calculation that determines the rate at which the present value of future cash flows from an investment equals the initial investment. It is not related to the emotional feeling of earning a return on your investment.

Question 14

One way to calculate the present value of a single payment is with the following formula: PV = FV × (1 + i)ⁿ.

Accepted Answer

The correct formula for calculating the present value (PV) of a single future payment (FV) is PV = FV / (1 + i)^n, where i is the interest rate and n is the number of periods.

Question 15

At the end of 8 years,your friend wants to have $50,000 saved for a down payment on a house.He expects to earn 8%-compounded monthly-on his investments over the next 8 years.How much would your friend have to put in his investment account each month to reach his goal?

Accepted Answer

To solve this, we use the formula for the future value of a series: $FV = P \times \frac{(1 + r)^n - 1}{r}$, where FV is the future value, P is the monthly payment, r is the monthly interest rate, and n is the total number of payments. Here, FV = $50,000, r = 0.08/12 (since it's compounded monthly), and n = 8*12 (8 years, 12 months each). Rearranging the formula to solve for P gives us the monthly payment needed to reach the goal. Plugging in the values, we find that the monthly payment is approximately $374.

Question 16

If you saw a table containing the following factors,what kind of interest factor would you be looking at?

Accepted Answer

The answer of If you saw a table containing the...

Question 17

A deposit placed in an interest-earning account earning 8% a year will double in value in ________ years.

Accepted Answer

The time required for the deposit to double can be calculated using the rule of 72 which states that the number of years required to double an investment is approximately equal to 72 divided by the annual interest rate (in percentage). 
So, in this case, 72 divided by 8 is 9. Therefore, the deposit will double in value in 9 years.

Question 18

In order to solve a compounding problem,you must know all four of the variables in order to solve for the fifth variable.

Accepted Answer

In a compounding problem, the four variables are principal (P), interest rate (r), time (t), and amount (A). In order to solve for the fifth variable, you need to know the other four.

Question 19

You always see an ordinary annuity used in business and never see an annuity due used in business.

Accepted Answer

An annuity due is also used in business. For example, a company may make regular payments for salaries, rent, or lease agreements at the beginning of each period, making it an annuity due.

Question 20

The future value of $1,000 compounded annually for 8 years at 12% may be calculated with the following formula: FV = $1,000 * (1 + 12%)⁸ If the same $1,000 was compounded quarterly,what formula would you use to calculate the FV?

Accepted Answer

When compounding quarterly, we need to adjust the interest rate by dividing it by 4 and also multiply the number of years by 4. Therefore, the formula would be FV = $1,000 * (1 + 3%)^(4*8) = $1,000 * (1 + 3%)^32, which is equivalent to FV = $1,000 * (1 + 12%)^8 as in option C.

Quiz 3: Mortgage Loan Foundations: The Time Value of Money

If you deposit $1,000 in an account that earns 5% per year (compounded monthly) ,what will the balance in the account be at the end of 5 years?

Assuming an interest rate of 6%,the present value of $1 that will be received a year from now is $0.75.

The future value compound factor given for period (n) at 15%:

The future value of a single deposit of $1,000 will be greatest when this amount is compounded:

Ten years ago,you put $150,000 into an interest-earning account.Today it is worth $275,000.What is the effective annual interest earned on the account?

Assume that an investment,with a single initial cost of $1,000 and a yield of $50 monthly for 10 years,had a 7% IRR in the 60th month and a 7.2% IRR five months later.The IRR can be 6.8% in the 62nd month.

The future value of $800 deposited today would be greater if that deposit earned 8% rather than 7.75%.

Your friend just won the lottery.He has a choice of receiving $50,000 a year for the next 20 years or a lump sum today.The lottery uses a 15% discount rate.What would be the lump sum amount your friend would receive?

The future value of a $1 annuity compounded at 5% annually is greater than the future value of a $1 annuity compounded at 5% semi-annually.

An investment may have more than one internal rate of return.

Begin with a single sum of money at period 0.First,calculate a future value of that sum at 12.01%.Then discount that future value back to period 0 at 11.99%.In relation to the initial single sum,the discounted future value:

The internal rate of return is the good feeling you get inside when you earn a return on your investment.

One way to calculate the present value of a single payment is with the following formula: PV = FV × (1 + i)ⁿ.

At the end of 8 years,your friend wants to have $50,000 saved for a down payment on a house.He expects to earn 8%-compounded monthly-on his investments over the next 8 years.How much would your friend have to put in his investment account each month to reach his goal?

If you saw a table containing the following factors,what kind of interest factor would you be looking at?

A deposit placed in an interest-earning account earning 8% a year will double in value in ________ years.

In order to solve a compounding problem,you must know all four of the variables in order to solve for the fifth variable.

You always see an ordinary annuity used in business and never see an annuity due used in business.

The future value of $1,000 compounded annually for 8 years at 12% may be calculated with the following formula: FV = $1,000 * (1 + 12%) ⁸ If the same $1,000 was compounded quarterly,what formula would you use to calculate the FV?

Quiz 3: Mortgage Loan Foundations: The Time Value of Money

If you deposit $1,000 in an account that earns 5% per year (compounded monthly) ,what will the balance in the account be at the end of 5 years?

Assuming an interest rate of 6%,the present value of $1 that will be received a year from now is $0.75.

The future value compound factor given for period (n) at 15%:

The future value of a single deposit of $1,000 will be greatest when this amount is compounded:

Ten years ago,you put $150,000 into an interest-earning account.Today it is worth $275,000.What is the effective annual interest earned on the account?

Assume that an investment,with a single initial cost of $1,000 and a yield of $50 monthly for 10 years,had a 7% IRR in the 60th month and a 7.2% IRR five months later.The IRR can be 6.8% in the 62nd month.

The future value of $800 deposited today would be greater if that deposit earned 8% rather than 7.75%.

Your friend just won the lottery.He has a choice of receiving $50,000 a year for the next 20 years or a lump sum today.The lottery uses a 15% discount rate.What would be the lump sum amount your friend would receive?

The future value of a $1 annuity compounded at 5% annually is greater than the future value of a $1 annuity compounded at 5% semi-annually.

An investment may have more than one internal rate of return.

Begin with a single sum of money at period 0.First,calculate a future value of that sum at 12.01%.Then discount that future value back to period 0 at 11.99%.In relation to the initial single sum,the discounted future value:

The internal rate of return is the good feeling you get inside when you earn a return on your investment.

One way to calculate the present value of a single payment is with the following formula: PV = FV × (1 + i)n.

At the end of 8 years,your friend wants to have $50,000 saved for a down payment on a house.He expects to earn 8%-compounded monthly-on his investments over the next 8 years.How much would your friend have to put in his investment account each month to reach his goal?

If you saw a table containing the following factors,what kind of interest factor would you be looking at?

A deposit placed in an interest-earning account earning 8% a year will double in value in ________ years.

In order to solve a compounding problem,you must know all four of the variables in order to solve for the fifth variable.

You always see an ordinary annuity used in business and never see an annuity due used in business.

The future value of $1,000 compounded annually for 8 years at 12% may be calculated with the following formula: FV = $1,000 * (1 + 12%) 8 If the same $1,000 was compounded quarterly,what formula would you use to calculate the FV?

One way to calculate the present value of a single payment is with the following formula: PV = FV × (1 + i)ⁿ.

The future value of $1,000 compounded annually for 8 years at 12% may be calculated with the following formula: FV = $1,000 * (1 + 12%) ⁸ If the same $1,000 was compounded quarterly,what formula would you use to calculate the FV?