FIN 3403 Ch 4

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?

$3,346.90

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?

$3,641.14

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

$3,920.14 To calculate the FV of a single sum you use the following formula; 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 Always consider whether your answer is even possible. For example a future value will always be more than the present value for any positive rate of interest. Remember to use a timeline to identify the timing and amount of each cash flow.

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?

$386.65 PMT = the monthly car payment PV = present value i = interest rate n = number of periods 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. What you are actually calculating is the annuity that is equivalent to $20,000 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%?

$7,743.60

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%?

$833.33. Perpetuity values are simply the cash flow, CF, divided by the required return, i; so: PV of a perpetuity = CF/i PV of a perpetuity = $100/0.12 = $833.33 You would be willing to pay $833.33 for this bond.

What is the present value of an ordinary annuity of $500 a year for 6 years assuming an interest rate of 9%?

$2,242.96

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?

5.1289% PV = -$1,000 since you are depositing the money. FV = $1,350 N = 6 PMT = 0 Solve for I/Y = 5.1289% annual return. You can easily check your result by the using the following formula for future value of a single sum. FV = PV(1 + i)n so $1,000(1.051289)6 = $1,350.08.

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 This problem is easy to solve using a financial calculator. Use the following inputs. PV = -12,000 FV = 30,000 I/Y = 10 PMT = 0 Solve for N = 9.6 years

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

Compounding is the process of:

Finding the future value of some amount when interest is reinvested

The __________ can be a useful rule of thumb when trying to determine how long it takes for some amount to double.

Rule of 72

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

Zeke will have $7,586.11 at the end of 7 years if he can earn 6% compounded quarterly on his initial $5,000 investment. This problem has quarterly compounding so you need to make some minor adjustments to the inputs before using the following future value formula; FV = PV(1 + i)n The annual interest rate needs converted to a quarterly interest rate and the number of periods needs converted from annual to quarterly as well. So, the quarterly interest rate is .06/4 = .015 per quarter. And, there are 28 quarters in a 7 year period (7 years x 4 quarter per year = 28). So, FV = $5,000(1 +.015)28 = $7,586.11

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%?

$1,049.33 This calculation is simple with your financial calculator. You must first convert the interest rate and number of periods to monthly. So, N will be 30 years x 12 months per year = 360 months. The I/Y will be 4.8%/12 = .4% per month. Keep in mind you are only financing $200,000 of the purchase price of the home. The calculator inputs will be; PV = $200,000 N = 360 I/Y = .4 FV = 0 Solve for PMT = -1,049.33 You can use the formula method to solve this problem but the financial calculator makes this a very quick and easy solution. Learn to use your financial calculator.

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?

$1,160.00 Simple interest refers to earning interest only on the original principal so this investor will earn $80 in interest ($1,000 x .08 = $80) for each year the $1,000 remains on deposit. In this case the $1,000 remains invested for two years so the investor will have the original $1,000 + $80 interest from year 1 + $80 interest from year two for a total of $1,160. Compound interest, or the process of earning interest on the principal and reinvested interest, would result in the investor accumulating $1,166.40 by the end of two years. The process of computing the compound interest amount is FV = PV(1 + i)n = $1,000(1.08)2 = $1,166.40.

What it 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?

$1,727.68

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?

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

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. To calculate the PV of an uneven cash flow stream you calculate the present values of the individual cash flows and sum those together. Look at the following timeline to help visualize the timing of these cash flows. In this case they are; = 776.70 + 2,827.79 + 1,372.71 = $4,977.20 Keep in mind that the present value in this example would always be less than the sum of the actual cash flows ($5,300) for any positive interest rate.

What is the present value of an annuity due of $2,000 a year for 3 years assuming an interest rate of 7%?

$5,616.03

An annuity refers to a series of:

Equal cash flows occurring at equal intervals for a finite period

The present value is equivalent to:

The value of a cash flow today