Emily Dorsey\'s current salary is $73,000 per year, and she is planning to retir

Question

Emily Dorsey's current salary is $73,000 per year, and she is planning to retire 20 years from now. She anticipates that her annual salary will increase by $2,000 each year ($73,000 the first year, to $75,000 the second year, $77,000 the third year, and so forth), and she plans to deposit 5% of her yearly salary into a retirement fund that earns 7% interest compounded daily. What will be the amount of interest accumulated at the time of Emily's retirement? Assume 365 days per year. The amount of interest accumulated at the time of Emily's retirement will be $thousand. (Round to the nearest whole number.)

Explanation / Answer

ANSWER:

retirement fund is 5% of salary

I = 7%

N = 365

er = (1 + i / n ) ^ n - 1

er = (1 + 7% / 365) ^ 365 - 1

er = (1 + 0.000191781) ^ 365 - 1

er = (1.000191781) ^ 365 - 1

er = 1.0725 - 1

er = 0.0725 or 7.25%

since the calculations are really long i have solved in excel using the npv function.

=npv(rate,all the cash flows of the retirement fund)

=npv(7.25%,3650,3750,3850,3950,4050,4150,4250,4350,4450,4550,4650,4750,4850,4950,5050,5150,5250,5350,5450,5550)

=$45,456.72

now we will find the future worth.

fw = pw(f/p,i,n)

fw = 45,456.72(f/p,7.25%,20)

fw = 45,456.72 * 4.05

fw = $184,307.97

so the retirement fund is $184,307.97

year 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 salary 73,000 75,000 77,000 79,000 81,000 83,000 85,000 87,000 89,000 91,000 93,000 95,000 97,000 99,000 101,000 103,000 105,000 107,000 109,000 111,000 retirement fund 3650 3750 3850 3950 4050 4150 4250 4350 4450 4550 4650 4750 4850 4950 5050 5150 5250 5350 5450 5550

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