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1) you believe you will need to have saved 500,000$ by the time you retire in 40

ID: 2613222 • Letter: 1

Question

1) you believe you will need to have saved 500,000$ by the time you retire in 40 years in order to live comfortably. if the interest rate is 6% per year, how much must you save each year to meet your retirement goal?

2)You believe you will spend 40,000$ a year for 20 years once you retire in 40 years. if the interest rate is 6% per year,how much must you save each year until retirement to meet your retirment goal ?

3) a couple thinking about retirement decide to put aside 3000$ each year in a savings plan that earns 8% interest. In 5 years they will receivve a gift of 10,000$ that also can be invested.

a) how much money will they have accumulated 30 years from now ?

b)if their goal is to retire with 800,000$ of savings, how much extra do they to save every year?

Explanation / Answer

Answer:1) The future value of the payments into your savings fund must accumulate to $500,000.

We choose the payment (C) so that:

C future value of an annuity = $500,000

Using a financial calculator, enter n = 40, i = 6, PV = 0, FV = 500,000; compute PMT = $3,230.77

Answer:2) By the time you retire you will need:

PV= The future value of the payments into your savings fund must accumulate to $458,796.85.

We choose the payment (C)

$40,000 × annuity factor(6%, 20 periods) = $458,769.85

The future value of the payments into your savings fund must accumulate to $458,769.85.

We choose the payment so that

PMT × future value of an annuity = $458,769.85

Using a financial calculator, enter n = 40, i = 6, PV = 0, FV = 458,796.85; compute PMT = $2,964.53

Answer:3)

a)After 30 years, the couple will have accumulated the future value of a $3,000 annuity, plus the future value of the $10,000 gift. The sum of the savings from these sources is:

$3,000 × Annuity factor (30, 8%) = $339,849.63

$10,000 × 1.08 25 = $68,484.75

$339,849.63 + $68,484.75 = $408,334.38 .

b) If they wish to accumulate $800,000 by retirement, they have to save an additional amount per year to provide additional accumulations of: $391,665.62 This requires additional annual savings of: $3,457.40

[Using a financial calculator, enter: i = 8; n = 30; PV = 0; FV = 391,665.62 and compute PMT.]