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Business Math Homework 13
Complete the ordinary annuity as an
annuity due for the following.
(Please use the following provided Table.) (Do not round intermediate calculations. Round your answer to the nearest cent.)
Complete the following for the present value of an ordinary annuity. (Use Table 13.2.) (Do not round intermediate calculations. Round your answer to the nearest cent.)
Using the annuity table, complete the
following.
(Use Table 13.2). (Do not round intermediate calculations. Round your answer to the nearest cent.)
Financial analysts recommend investing 15% to 20% of your annual income in your retirement fund to reach a replacement rate of 70% of your income by age 65. This recommendation increases to almost 30% if you start investing at 45 years old. Mallori Rouse is 25 years old and has started investing $3,600 at the end of each year in her retirement account. How much will her account be worth in 20 years at 11% interest compounded annually? How much will it be worth in 30 years? What about at 40 years? How much will it be worth in 50 years? (Please use the following provided Table 13.1.) (Do not round intermediate calculations. Round your answers to the nearest whole dollar amount.)
You are earning an average of $47,000 and will retire in 12 years. If you put 25% of your gross average income in an ordinary annuity compounded at 6% annually, what will be the value of the annuity when you retire? (Please use the following provided Table.) (Do not round intermediate calculations. Round your answer to the nearest cent.) Annuity value $ 198,221.33 
You decide to reduce the amount you spend eating out by $240 a month and invest the total saved at the end of each year in your retirement account. How much will the account be worth at 5% in 30 years? (Use Table 13.1.) (Do not round intermediate calculations. Round your answer to the nearest cent.) Future value after 30 years $ 191,343.17
Ed Long promised to pay his son $340 semiannually for 11 years. Assume Ed can invest his money at 6% in an ordinary annuity. How much must Ed invest today to pay his son $340 semiannually for 11 years? (Please use the following provided Table.) (Do not round intermediate calculations. Round your answer to the nearest cent.) Present value $ 5,418.55
====================================== Al Vincent has decided to retire to Arizona in 11 years. What amount should Al invest today so that he will be able to withdraw $30,000 at the end of each year for 16 years after he retires? Assume he can invest the money at 6% interest compounded annually. (Use the Table 13.2 and Table 12.3.) (Do not round intermediate calculations. Round your answer to the nearest cent.) Present value $ 159,713.64
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Homework Chapter 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 Need A Tutor? Need Homework Help? On Joe Martin’s graduation from college, Joe’s uncle promised him a gift of $11,600 in cash or $760 every quarter for the next 3 years after graduation. Assume money could be invested at 8% compounded quarterly. (Use Table 13.2.) a. Calculate the present value of options. (Do not round intermediate calculations. Round your answer to the nearest cent.)
b. Which offer is better for Joe? Option 1
Bankrate.com reported on a shocking statistic: only 53% of workers participate in their company’s retirement plan. This means that 47% do not. With such an uncertain future for Social Security, this can leave almost 1 in 2 individuals without proper income during retirement. Jill Collins, 30, decided she needs to have $300,000 in her retirement account upon retiring at 60. How much does she need to invest each year at 6% compounded annually to meet her goal? (Please use the following provided Table.) (Do not round intermediate calculations. Round your answer to the nearest dollar amount.) Each year investment $ 3,780
John Regan, an employee at Home Depot, made deposits of $730 at the end of each year for 6 years. Interest is 6% compounded annually. What is the value of John's annuity at the end of 6 years? (Use Table 13.1.) (Do not round intermediate calculations. Round your answer to the nearest cent.) 5,091.97 Explanation: 6 years × 1 = 6 periods 6/1=6% 6 periods, 6% $730 × 6.9753 = $5,091.97 Susan Orman wants to pay $1,480 semiannually to her granddaughter for 12 years for helping her around the house. If Susan can invest money at 6% compounded semiannually, how much must she invest today to meet this goal? (Please use the following provided Table.) (Do not round intermediate calculations. Round your answer to the nearest cent.) 25,064.54 Explanation: 12 years × 2 = 24 periods 6 / 2=3% 24 periods, 3% $1,480 × 16.9355 = $25,064.54 Financial analysts recommend investing 15% to 20% of your annual income in your retirement fund to reach a replacement rate of 70% of your income by age 65. This recommendation increases to almost 30% if you start investing at 45 years old. Mallori Rouse is 25 years old and has started investing $4,800 at the end of each year in her retirement account. How much will her account be worth in 20 years at 6% interest compounded annually? How much will it be worth in 30 years? What about at 40 years? How much will it be worth in 50 years? (Please use the following provided Table 13.1.) (Do not round intermediate calculations. Round your answers to the nearest whole dollar amount.) Future value after 20 years: $176,570 Future value after 30 years: $379,478 Future value after 40 years: $742,856 Future value after 50 years: $1,393,608 Explanation Periods for 20 years: 20 × 1 = 20 Interest rate per period = 6% / 1 = 6% $4,800 × 36.7856 = $176,571 Periods for 30 years: 30 × 1 = 30 Interest rate per period = 6% / 1 = 6%$4,800 × 79.0582 = $379,479 Periods for 40 years: 40 × 1 = 40 Interest rate per period = 6% / 1 = 6%$4,800 × 154.7620 = $742,858 Periods for 50 years: 50 × 1 = 50Interest rate per period = 6% / 1 = 6%$4,800 × 290.3359 = $1,393,612 Josef Company borrowed money that must be repaid in 15 years. The company wants to make sure the loan will be repaid at the end of year 15. So it invests $11,600 at the end of each year at 10% interest compounded annually. What was the amount of the original loan? (Use Table 13.1.) (Do not round intermediate calculations. Round your answer to the nearest cent.) 368,561.00 Explanation: 15 years × 1 = 15 periods 10/ 1= 10% 15 periods, 10% $11,600 × 31.7725 = $368,561.00 $1,890 Explanation: Periods = 30 years × 1 = 30 periods Interest rate per period = 6%/1 = 6% $150,000 × 0.0126 = $1,890 each year
Alice Longtree
has decided to invest $480 quarterly for 3 years in an ordinary annuity
at 8%. As her financial adviser,
calculate for Alice the total cash value of the annuity at the end of
year 3. (Please use the following provided Table.) (Do not round
intermediate calculations. Round your answer to the nearest cent.)
6,437.81 Explanation: 3 years × 4 = 12 periods 8/2=4% 12 periods, 2% $480 × 13.4121 = $6,437.81 1,476.90 Explanation 7 years × 2 = 14 periods 8/2=4% 14 periods, 4% = 0.0547 $27,000 × 0.0547 = $1,476.90 Check: $1,476.90 × 18.2919 = $27,015.31 (due to table rounding)
On Joe Martin's graduation
from college, Joe's uncle promised him a gift of $12,900 in cash or
$810 every quarter for the next 4 years after graduation. Assume money
could be invested at 8% compounded quarterly. (Use Table 13.2.)a. Calculate the present value of options.
(Do not round intermediate calculations. Round your answers to the
nearest cent.)
Option 1: 12,900.00 Option 2: 10,997.94 Option 1 is the better offer for Joe. Explanation: Option 1, today's value is $12,900. Option 2: 4 years × 4 = 16 periods 8 / 4=2% $810 × 13.5777 = $10,997.94
Mike Macaro is selling a
piece of land. Two offers are on the table. Morton Company offered a
$34,000 down payment and $34,400 a year for the next 6 years. Flynn
Company offered $22,000 down and $39,600 a year for the next 6 years.
Assume money can be invested at 7% compounded annually. (Use Table
13.2.) a. What is the value of the offers? (Do not round intermediate
calculations. Round your answers to the nearest cent.) b. Which offer
is better for Mike?
Morton Company: $197,967.60 Flynn Company: $210,753.40 Flynn Company is the better offer for Mike. Explanation a. Morton: 6 periods, 7% 6 years × 1 = 6 periods 7%= 7%1 $34,400 × 4.7665 = $163,967.60 + $34,000 = $197,967.60 Flynn: 6 periods, 7% 6 years × 1 = 6 periods 7%= 7%1 $39,600 × 4.7665 = $188,753.40 + $22,000 = $210,753.40 b. Flynn offer is the better deal.
Victor
French made deposits of $4,800 at the end of each quarter to Book Bank,
which pays 8% interest compounded quarterly. After 3 years, Victor made
no more deposits. What will be the balance in the account 2 years after
the last deposit? (Use the Table and Table 12.1.) (Do not round
intermediate calculations. Round your answer to the nearest cent.)
$75,431.80 Explanation: Amount of annuity table: 3 years × 4 = 12 periods 8 / 4 = 2% (Table) $4,800 × 13.4121 = $64,378.08 Compound table: 2 years × 4 = 8 periods 8/4= 2% (Table 12.1) $64,378.08 × 1.1717 = $75,431.80 Janet Woo decided to retire to Florida in 5 years. What amount should Janet invest today so she can withdraw $54,000 at the end of each year for 20 years after she retires? Assume Janet can invest money at 5% compounded annually. (Use the Table 13.2 and Table 12.3.) (Do not round intermediate calculations. Round your answer to the nearest cent.) $527,263.22 Explanation: PV annuity table: 20 years × 1 = 20 periods 5%= 5% (Table 13.2) $54,000 × 12.4622 = $672,958.80 PV table: 5 years x 1 = 5 periods 5 / 1 = 5% $672,958.80 × 0.7835 = $527,263.22 Ajax Corporation has hired Brad O'Brien as its new president. Terms included the company's agreeing to pay retirement benefits of $18,100 at the end of each semiannual period for 11 years. This will begin in 3,650 days. If the money can be invested at 8% compounded semiannually, what must the company deposit today to fulfill its obligation to Brad? (Please use the following provided Table and Table 12.3.) (Use 365 days a year. Do not round intermediate calculations. Round your answer to the nearest cent.) $119,378.22 Explanation: 11 years x 2 = 22 periods 8/2 = 4% $18,100 × 14.4511 = $261,564.91 3,650 days/365 days per year = 10 years 10 years x 2 = 20 periods 8/2 = 4% $261,564.91 × 0.4564 = $119,378.22 |
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