Question

A rich relative has bequeathed you a growing perpetuity. The first payment will occur in a year and will be $1,000. Each year after that, you will receive a payment on the anniversary of the last payment that is 6% larger than the last payment. This pattern of payments will go on forever. What is value (in $) of the bequest today if the interest rate is 11% per year?

$

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You are thinking of building a new machine that will save you $1,000 in the first year. The machine will then begin to wear out so that the savings decline at a rate of 5% per year forever. What is the present value (in $) of the savings if the interest rate is 2% per year? (Round your answer to the nearest cent.)

$

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Assume that Social Security promises you $30,000 per year starting when you retire 45 years from today (the first $30,000 will come 45 years from now). If your discount rate is 6%, and you expect to live for 15 years after retiring (so that you will get a total of 16 payments including the first one), what is the value today of Social Security's promise (in $)? (Round your answer to the nearest cent.)

$

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Suppose that a young couple has just had their first baby and they wish to ensure that enough money will be available to pay for their child's college education. They decide to make deposits into an educational savings account on each of their daughter's birthdays, starting with her first birthday until her 18th birthday. The parents deposit $3,500 on their daughter's first birthday and plan to increase the size of their deposits by 5% each year. Assume that the educational savings account will return a constant 6%.

How much will the parents deposit (in $) on the second birthday?

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How much will the parents deposit (in $) on the 18th birthday? (Round your answer to the nearest cent.)

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What is the total balance available for their daughter's college expenses (in $) on her 18th birthday right after they make their 18th and final deposit? (Round your answer to the nearest cent.)

$

Answer 1

HI

As per policy we will solve only first question here.

Here This is example of growing perpetuity

first payment C1 = $1000

growth rate g = 6%

interest rate r = 11%

Present Value of perpetuity = C1/(r-g)

=1000/(11%-6%)

= $20,000

Thanks