# Answered Essay: Emily Dorsey's current salary is \$77.000 per year, and she is planning to retire 29 years from now. She anticipates that her an

Emily Dorsey’s current salary is \$77.000 per year, and she is planning to retire 29 years from now. She anticipates that her annual salary will increase by \$2,000 each year (\$77,000 the first year, to \$79.000 the second year, \$81.000 the third year, and so forth), and she plans to deposit 5% of her yearly salary into a retirement fund that earns 8% interest compounded daily. What will be the amount of interest accumulated at the time of Emily’s retirement? Assume 365 days per year.

Solution:

Suppose Emily Current Age is 20

And Current Salary is \$77,000

She can invest 5% of the salary per year @8% compounding daily

Future Value of at age 29 = Present Value * { 1 + (interest rate/compounding frequency)}^( number of year you leave to invest * compounding frequency)

Or FV = PV * {1+(r/m)}^(t*m) 1st Year investment value after 29 years = 3850*{1+(.08/365)}^(7*365)

=3850*2.05427

=\$7,908.94

2nd year investment value = 3950*(1.000219)^(8*365)

=3950*1.89635

=\$7490.57

3rd Year investment Value =4050*(1.000219)^(7*365)

=\$7089.79

4th Year investment Value

= 4150*(1.000219)^(6*365)

=\$6,706.36

5th Year investment value =4250*(1.000219)^(5*365)

=\$6339.98

6th year investment value

= 4350*(1.000219)^(4*365)

=\$5852.59

7th Year investment value =4450*(1.000219)^(3*365)

=\$5656.91

8th year investment value = 4550*(1.000219)^(2*365)

=5339.38

9th year investment value = 4650*(1.000219)^365 =5073.24

So, total value of investment = 7908.94+7490.57+7089.79+6706.36+6339.98+5852.59+5656.91+5339.38+5073.24 = 57457.76

Total investment = 3850+3950+4050+4150+4250+4350+4450+4550+4650 = 38250

Interest Accumulated = 57458-38250 = 19,208

Total retirement fund = \$57,458

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