What is the future value of $1,730 in 15 years assuming an interest rate of 7.00 percent compounded

What is the future value of $1,730 in 15 years assuming an interest rate of 7.00 percent compounded semiannually? (Do not include the dollar sign ($). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Future value

$

rev: 04-30-2011

Explanation:

For this problem, we simply need to find the FV of a lump sum using the equation:

FV = PV(1 + r)t

It is important to note that compounding occurs semiannually. To account for this, we will divide the interest rate by two (the number of compounding periods in a year), and multiply the number of periods by two. Doing so, we get:

FV = $1,730[1 + (0.0700/2)]30

FV = $4,855.75

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Enter

15 × 2

7.00% / 2

±$1,730

N

I/Y

PV

PMT

FV

Solve for

$4,855.75

 

Curly’s Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs

Curly’s Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $31,000 per year forever. Suppose Curly’s told you the policy costs $560,000.

Required:

At what interest rate would this be a fair deal? (Do not include the percent sign (%). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Interest rate

%

Explanation:

Here we need to find the interest rate that equates the perpetuity cash flows with the PV of the cash flows. Using the PV of a perpetuity equation:

PV = C / r

$560,000 = $31,000 / r

We can now solve for the interest rate as follows:

r = $31,000 / $560,000

r = 0.0554 or 5.54%

Curly’s Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs

Curly’s Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $25,000 per year forever. Assume the required return on this investment is 7.9 percent.

Required:

How much will you pay for the policy? (Do not include the dollar sign ($). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Paid for the policy

$

Explanation:

This cash flow is a perpetuity. To find the PV of a perpetuity, we use the equation:

PV = C / r

PV = $25,000 / 0.079

PV = $316,455.70

You want to have $32,000 in your savings account ten years from now, and you’re prepared to make

You want to have $32,000 in your savings account ten years from now, and you’re prepared to make equal annual deposits into the account at the end of each year.

Required:

If the account pays 6.50 percent interest, what amount must you deposit each year? (Do not include the dollar sign ($). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Amount to be deposit

$

rev: 04-30-2011

Explanation:

Here we have the FVA, the length of the annuity, and the interest rate. We want to calculate the annuity payment. Using the FVA equation:

FVA = C{[(1 + r)t – 1] / r}

$32,000 = C[(1.065010 – 1) / 0.0650]

We can now solve this equation for the annuity payment. Doing so, we get:

C = $32,000 / 13.49442

C = $2,371.35

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Enter

10

6.50%

±$32,000

N

I/Y

PV

PMT

FV

Solve for

$2,371.35

 

If you put up $30,000 today in exchange for a 8.4 percent, 9-year annuity, what will the annual cash

If you put up $30,000 today in exchange for a 8.4 percent, 9-year annuity, what will the annual cash flow be? (Do not include the dollar sign ($). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Annuity cash flow

$

rev: 04-30-2011

Explanation:

Here we have the PVA, the length of the annuity, and the interest rate. We want to calculate the annuity payment. Using the PVA equation:

PVA = C({1 – [1/(1 + r)t]} / r )

$30,000 = C{[1 – (1/1.084)9 ] / 0.084}

We can now solve this equation for the annuity payment. Doing so, we get:

C = $30,000 / 6.14430

C = $4,882.57

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Enter

9

8.4%

±$30,000

N

I/Y

PV

PMT

FV

Solve for

$4,882.57

Havana, Inc., has identified an investment project with the following cash flows.

Havana, Inc., has identified an investment project with the following cash flows.

Year	Cash Flow
1		$	980
2			1,210
3			1,430
4			2,170

Requirement 1:

Assume the discount rate is 6 percent, what is the future value of these cash flows in Year 4? (Do not include the dollar sign ($). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Future value

$

Requirement 2:

What is the future value at an interest rate of 14 percent? (Do not include the dollar sign ($). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Future value

$

Requirement 3:

What is the future value at an interest rate of 21 percent? (Do not include the dollar sign ($). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Future value

$

rev: 04-30-2011

Explanation:

To solve this problem, we must find the FV of each cash flow and sum. To find the FV of a lump sum, we use:

FV = PV(1 + r)t

FV@6% = $980(1.06)3 + $1,210(1.06)2 + $1,430(1.06) + $2,170 = $6,212.55

FV@14% = $980(1.14)3 + $1,210(1.14)2 + $1,430(1.14) + $2,170 = $6,824.63

FV@21% = $980(1.21)3 + $1,210(1.21)2 + $1,430(1.21) + $2,170 = $7,407.99

Notice, since we are finding the value at Year 4, the cash flow at Year 4 is simply added to the FV of the other cash flows. In other words, we do not need to compound this cash flow.

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

CFo	$0	CFo	$0	CFo	$0
C01	$980	C01	$980	C01	$980
F01	1	F01	1	F01	1
C02	$1,210	C02	$1,210	C02	$1,210
F02	1	F02	1	F02	1
C03	$1,430	C03	$1,430	C03	$1,430
F03	1	F03	1	F03	1
C04	$2,170	C04	$2,170	C04	$2,170
F04	1	F04	1	F04	1
I = 6		I = 14		I = 21
NPV CPT		NPV CPT		NPV CPT
$6,212.55		$6,824.63		$7,407.99

Zevon Co. has identified an investment project with the following cash flows.

Zevon Co. has identified an investment project with the following cash flows.

Year	Cash Flow
1		$	1,190
2			1,090
3			1,540
4			1,900

Requirement 1:

Assume the discount rate is 10 percent, what is the present value of these cash flows? (Do not include the dollar sign ($). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Present value

$

Requirement 2:

What is the present value at 18 percent? (Do not include the dollar sign ($). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Present value

$

Requirement 3:

What is the present value at 24 percent? (Do not include the dollar sign ($). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Present value

$

rev: 04-30-2011

Explanation:

To solve this problem, we must find the PV of each cash flow and add them. To find the PV of a lump sum, we use:

PV = FV / (1 + r)t

PV@10% = $1,190 / 1.10 + $1,090 / 1.102 + $1,540 / 1.103 + $1,900 / 1.104 = $4,437.39

PV@18% = $1,190 / 1.18 + $1,090 / 1.182 + $1,540 / 1.183 + $1,900 / 1.184 = $3,708.59

PV@24% = $1,190 / 1.24 + $1,090 / 1.242 + $1,540 / 1.243 + $1,900 / 1.244 = $3,279.93

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

CFo	$0	CFo	$0	CFo	$0
C01	$1,190	C01	$1,190	C01	$1,190
F01	1	F01	1	F01	1
C02	$1,090	C02	$1,090	C02	$1,090
F02	1	F02	1	F02	1
C03	$1,540	C03	$1,540	C03	$1,540
F03	1	F03	1	F03	1
C04	$1,900	C04	$1,900	C04	$1,900
F04	1	F04	1	F04	1
I = 10		I = 18		I = 24
NPV CPT		NPV CPT		NPV CPT
$4,437.39		$3,708.59		$3,279.93