Question 1

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

Accepted Answer

The definition given is incorrect. The internal rate of return (IRR) is a financial metric used to calculate the profitability of an investment, taking into account the time value of money. It is the discount rate that makes the net present value (NPV) of all cash flows from an investment equal to zero.

Question 2

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, the interest rate per period is 12%/4 = 3%. Therefore, the correct formula would be FV = $1,000 * (1 + 3%)^(8*4) = $1,000 * (1.03)^32 = $2,011.36. Choice A is incorrect because it uses the same formula as the annual compounding but with the wrong interest rate. Choice B uses the formula for monthly compounding, which is not applicable to quarterly compounding. Choice D uses the formula for semi-annual compounding, which also does not apply in this case.

Question 3

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 4

At 6%, the present value of a $1 payment in 12 months is .941905. At 7%, the present value of a $1 payment in 12 months is .950342.

Accepted Answer

The present value of a future payment decreases as the discount rate increases. Therefore, at 7%, the present value should be less than at 6%, not more.

Question 5

If you saw a table containing the following factors, what kind of interest factor would you be looking at? $\begin{array}{ccc}
\text { End of Year } & & {6 \%} \
\hline 1 & & 1.06000 \
2 & & 1.12360 \
3 & & 1.1910 \
4 & & 1.2624 \
5 & & 133822
\end{array}$

Accepted Answer

The table shows the future value of a single amount, as it lists the accumulated value at the end of each year when compounded annually at a 6% interest rate.

Question 6

If you deposit $1,000 in an account that earns 5% per year, compounded annually, you will have $1,276 at the end of 5 years. What would be the balance in the account at the end of 5 years if interest compounds monthly?

Accepted Answer

When interest is compounded monthly, the formula used is A = P(1 + r/n)^(nt), where P is the principal amount ($1,000), r is the annual interest rate (0.05), n is the number of times interest is compounded per year (12), and t is the number of years (5). Plugging in these values, the balance is approximately $1,283.

Question 7

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 to calculate the present value of a single payment is PV = FV / (1+i)^n, where PV is the present value, FV is the future value, i is the discount rate, and n is the number of periods.

Question 8

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

Accepted Answer

The more frequently interest is compounded, the greater the future value will be. Monthly compounding results in the highest frequency of compounding among the given options, leading to the greatest future value.

Question 9

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

Accepted Answer

This is because the higher the interest rate, the quicker the money will grow over time. Therefore, the future value of $800 will be greater if it earns interest at a higher rate of 8% compared to 7.75%.

Question 10

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

Accepted Answer

This can occur when a project has multiple cash inflows and outflows that result in changes in the sign of cash flows. In these cases, the investment could have multiple points where the net present value of cash flows equals zero, resulting in multiple internal rates of return.

Question 11

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 12

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

Accepted Answer

An annuity due is actually used in business, particularly in situations where payments or receipts occur at the beginning of each period instead of at the end. Examples include rent payments, lease payments, and certain types of mortgages.

Question 13

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

When compounding semi-annually, the interest is applied twice a year, resulting in a higher effective interest rate. Therefore, the future value of a $1 annuity compounded at 5% semi-annually will be greater than the future value of a $1 annuity compounded annually at 5%.

Question 14

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

Since the future value is calculated at a higher interest rate (12.01%) than the discount rate (11.99%), it will be higher than the original single sum. And since it is then discounted back to period 0 at a slightly lower rate (11.99%), it will still be higher than the original amount. Therefore, the discounted future value will be greater than the original amount.

Question 15

Assume that an investment, with an 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

The IRR (Internal Rate of Return) is a single rate that makes the net present value of cash flows equal to zero over the entire investment period. It cannot fluctuate monthly once calculated for a specific period.

Question 16

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

Accepted Answer

Using the Rule of 72, which is a simplified way to estimate the number of years required to double the investment at a fixed annual rate of interest, you divide 72 by the interest rate. For an 8% interest rate, 72/8 = 9 years.

Question 17

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

In order to calculate the present value of the future sum of $100,000, we need to use the formula: PV = FV/(1+i)^n, where PV is the present value, FV is the future value, i is the interest rate, and n is the number of years. In this case, n=10, i=20%, and FV= $100,000. Plugging in these values, we get:

PV= $100,000/(1+0.2)^10 
PV= $100,000/6.1917 
PV= $16,151.

Therefore, you should be willing to lend your friend $16,151 today in exchange for his trust fund.

Question 18

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

Accepted Answer

The future value compound factor increases with an increase in the number of periods and the compound interest rate. Since the factor for period n+1 has a higher number of periods than the factor for period n, it would be greater. Therefore, the factor for period n would be less than the factor for period n+1 at the same interest rate.

Question 19

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 your friend would receive?

Accepted Answer

The lump sum is the present value of the annuity. Using the formula for the present value of an annuity: PV = Pmt * [(1 - (1 + r)^-n) / r], where Pmt = $50,000, r = 0.15, and n = 20, the calculation gives approximately $312,967.

Question 20

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 $. Solving for $ r $ when $ A = 275,000 $, $ P = 150,000 $, and $ n = 10 $ gives approximately 6.25%.

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

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

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?

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?

At 6%, the present value of a $1 payment in 12 months is .941905. At 7%, the present value of a $1 payment in 12 months is .950342.

If you saw a table containing the following factors, what kind of interest factor would you be looking at? $\begin{array}{ccc}\text { End of Year } & & {6 \%} \\\hline 1 & & 1.06000 \\2 & & 1.12360 \\3 & & 1.1910 \\4 & & 1.2624 \\5 & & 133822\end{array}$

If you deposit $1,000 in an account that earns 5% per year, compounded annually, you will have $1,276 at the end of 5 years. What would be the balance in the account at the end of 5 years if interest compounds monthly?

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 a single deposit of $1,000 will be greater when this amount is compounded:

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

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

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

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:

Assume that an investment, with an 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.

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

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

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 your friend would receive?

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?

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

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

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?

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?

At 6%, the present value of a $1 payment in 12 months is .941905. At 7%, the present value of a $1 payment in 12 months is .950342.

If you deposit $1,000 in an account that earns 5% per year, compounded annually, you will have $1,276 at the end of 5 years. What would be the balance in the account at the end of 5 years if interest compounds monthly?

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 a single deposit of $1,000 will be greater when this amount is compounded:

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

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

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

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:

Assume that an investment, with an 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.

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

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

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 your friend would receive?

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?

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.