FINA 3313 Ch.5 DSM

What is the value three years from now of $3,200 deposited today that will earn an annual return of 7%?

$1,727.68

What is the present value of $2,000 that you expect to receive in 3 years assuming you could invest the money today and earn a 5% annual return?

$1727.68

How much will your monthly payment be if you purchase a home for $221,000 and you finance $200,000 for 30 years at 4.8%?

PV = $200,000 N = 360 I/Y = .4 FV = 0 Solve for PMT = -1,049.33

How much will you accumulate in an account where you deposit $1,100 a year at the beginning of the next 3 years if you can earn 5% annually?

$3,346.90 by the end of the fourth year. To calculate the FV of an ordinary annuity you use the following formula;

What is the present value of $800 to be received at the end of year one, $3,000 at the end of year two, and $1,500 at the end of year three assuming a discount rate of 3%?

$4,977.20

How much will Zeke have at the end of 7 years if he can earn 6% compounded quarterly on his initial $5,000 investment?

$7,586.11

An investment with a nominal annual rate of interest of 5% and semi-annual compounding will yield an effective annual rate of ______.

5.06%

What is the effective annual rate (EAR) of interest for an account that has an annual percentage rate (APR) of 8% that is compounded quarterly?

8.243%

How many years will it take you to accumulate $30,000 for a down payment on a house if you deposit $12,000 today and you expect to earn a 10% annual return on your investment?

9.6 years

What is the present value of $800 to be received at the end of year one, $3,000 at the end of year two, and $1,500 at the end of year three assuming a discount rate of 3%?

= 776.70 + 2,827.79 + 1,372.71 = $4,977.20

One technique often used in time value of money problems that provides a linear representation of cash flows is:

A timeline

When the payment of an annuity occurs at the beginning of the period instead of at the end of the period it is known as:

An annuity due

Discounting cash flows refers to:

Calculating the present value of cash flows to be received at some point in the future

An annuity refers to a series of:

Equal cash flows occurring at equal intervals for a finite period

Elizabeth wants to have $500,000 saved for retirement in 20 years. Assuming she can earn an 8% annual return on her investments how much will she need to save at the end of each of the next 20 years to accomplish her goal?

FV = 500,000 N = 20 I/Y = 8 PV = 0 Solve for PMT = -10,926.10

What is the value three years from now of $3,200 deposited today that will earn an annual return of 7%?

FV = PV(1 + i)n where; FV = future value PV = present value i = interest rate n = number of periods So, FV = $3,200(1 + .07)3 = $3,200(1.22504) = $3,920.14

How much will an investor accumulate by the end of two years if she deposits $1,000 in an account earning 8% annual simple interest?

FV = PV(1 + i)n = $1,000(1.08)2 = $1,166.40.

If you can invest $1,000 today and it will grow to be worth $1,350 over the next 6 years, what is the compound annual return you will earn on this investment?

FV = PV(1 + i)n = $1,000(1.08)2 = $1,166.40.

How much will you accumulate in an account where you deposit $800 a year at the end of the next 4 years if you can earn 3% annually?

FV=PMTx[(1+r)^n-1/i] $3,346.90

Jim is considering buying a car that costs $20,000 that can be financed for 5 years at 6% interest with no down payment. How much will Jim's payment be per month?

In this example you need to convert the 5 years to 60 months (5 years x 12 months per year) and convert the 6% APR to 0.5% per month (6%/12 months = .5% per month). Making these conversions makes the problem consistent since now every input is a monthly input.

If you can invest $1,000 today and it will grow to be worth $1,350 over the next 6 years, what is the compound annual return you will earn on this investment?

PV = -$1,000 since you are depositing the money. FV = $1,350 N = 6 PMT = 0 Solve for I/Y = 5.1289% annual return.

What is the value of a bond that never matures that will generate an annual coupon payment of $100 assuming your required return is 12%?

PV of a perpetuity = $100/0.12 = $833.33

What is the value of a bond that never matures that will generate an annual coupon payment of $100 assuming your required return is 12%?

PV of a perpetuity = $100/0.12 = $833.33 Perpetuity-a bond or other security with no fixed maturity date.

If you can invest $1,000 today and it will grow to be worth $1,350 over the next 6 years, what is the compound annual return you will earn on this investment?

So, PV = -$1,000 since you are depositing the money. FV = $1,350 N = 6 PMT = 0 Solve for I/Y = 5.1289% annual return.

The concept that a dollar received today is worth more than a dollar received at some point in the future is known as:

The time value of money

The present value is equivalent to:

The value of a cash flow today

At the end of year three, what is the future value of $1,000 to be received at the end of year one, $2,000 to be received at the end of year two, and $4,500 to be received at the end of year three assuming an interest rate of 6%?

The year 1 cash flow will earn 6% for 2 years, from the end of year one to the end of year 3 so FV CF1 = $1,000(1.06)2 = $1,123.60. The year 2 cash flow will earn 6% for one year, from the end of year two to the end of year three so the FV CF2 = $2,000(1.06) = $2,120.00. The future value of $4,500 to be received in year three is simply the $4,500.00. Therefore the FV of the entire CF stream = $1,123.60 + $2,120.00 + $4,500.00 = $7,743.60.

At the end of year three, what is the future value of $1,000 to be received at the end of year one, $2,000 to be received at the end of year two, and $4,500 to be received at the end of year three assuming an interest rate of 6%?

The year 1 cash flow will earn 6% for 2 years, from the end of year one to the end of year 3 so FV CF1 = $1,000(1.06)2 = $1,123.60. The year 2 cash flow will earn 6% for one year, from the end of year two to the end of year three so the FV CF2 = $2,000(1.06) = $2,120.00. The future value of $4,500 to be received in year three is simply the $4,500.00. Therefore the FV of the entire CF stream = $1,123.60 + $2,120.00 + $4,500.00 = $7,743.60. Keep in mind that the future value in this example would always exceed the sum of the actual cash flows ($7,500) for any positive interest rate.

Compound interest is:

interest paid on the investment's original deposit and accumulated interest.