Time Value of Money II Worksheet 1 You want to be a million

Time Value of Money II - Worksheet

1. You want to be a millionaire in 25 years. If you earn 10% on your investments, how much do you have to see each year to hit the $1,000,000 mark?

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2. Amy is 65 and has $350,000 in her retirement account. An actuary has determined that if her investments earn 7%, she can withdraw $32,300 annually. How many more years does the actuary expect Amy to live?

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3.. Karla sued her landlord 5 years ago for damage to her things from a water leak and won a judgment against him.   The original award was $15,500, but she finally received $18,858, which included interest. What is the rate of interest she received?

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Ty bought a new car for $25,000. He put $2,000 down and financed the rest with the dealer who had a special offer of 2% interest for 60 monthly payments. How much will Ty pay each month?

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Twins Taylor and Tanner both received $1,000 from their grandmother for their birthday. She told them they had to save it for 5 years. Taylor found an account paying 4.5% with monthly compounding. Tanner elected an account paying 5% with annual compounding. Who will have more at the end of the five years?

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Piper has $300,000 for her retirement. She is considering investing in a 20-year, 7% annuity and is trying to determine whether she should take the payments quarterly or monthly. Under which method would she get the most money each year?

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Twins Kate and Allie will be going to college in 15 years. Their parents have decided that Dad will start a savings fund for Kate. He will deposit $2,000 into an account the first of each year. That account earns 7% and interest is compounded annually. Their mother will also deposit $2,000 into an account for Allie, but she is going to make those deposits at the end of each quarter and the account pays 7.5% compounded quarterly. Who will have more in her college fund?

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Solution

Solution 1:

Future value = $1,000,000

Let required annual earning = a

Now a * Cumulative FV factor of annuity due at 10% for 25 periods = $1,000,000

a * 98.34706 = $1,000,000

a = $10,168

I need to have $10,168 each year in order to become millanaire in 25 years.

Solution 2:

Let may live t years more so that balance in her account will be zero if she withdraw $32,300 annually.

Now present value of $32,300 at t periods = $350,000

$32,300 * Cumulative PV factor at 7% for t periods = $350,000

Cumulative PV factor at 7% for t periods = $350,000 / $32,300 = 10.83591

Cumulative PV factor falls at t = 21 years

Therefore actuary expect amy to live 21 more years

Solution 3:

Award amount (Principal) = $15,500

Amount received after 5 years (Future value) = $18,858

Let rate of interest = i

Now P (1+i)^n = $18,858

$15,500 (1+i)^5 = $18,858

(1+i)^5 = 1.21664

1+i = (1.21664)^1/5

i = 4%

Rate of interest = 4%

Solution 4:

Car price = $25,000

Down payment = $2,000

Loan amount = $25,000 - $2,000 = $23,000

rate of interest = 2%, 0.166666% monthly rate of interest

Total monthly payments = 60

Amount to be paid each month = $23,000 / Cumulative PV factor at 0.166666% for 60 periods

= $23,000 / 57.05236 = $403.14

Therefore monthly payment = $403.14

Note: I have answered first 4 parts of the question as per chegg policy. Kindly post separate question for answer of remaining questions.