Today, you turn 23. your birthday wish is that you will be a millionaire by your 40th birthday. in an attempt to reach this goal, you decide to save $75 a day, every day, until you turn 40. you open an investment account and deposit your first $75 today. what rate of return must you earn to achieve your goal? 7.67 percent 8.09 percent 9.90 percent 10.06 percent 10.54 percent

Since 13335.18058 is closest to 13333.33333, 8.09% is the interest rate I must earn to achieve my goal of becoming a millionaire.

The interest rates for Future Values and Present Values of annuities are always calculated by iteration.

Since we have four options we can substitute the value of r for each of the interest rates for each period.

In this question we have

Payment = $75

Frequency of saving : Daily

No. of years :  

So, number of periods =

The interest rate quoted usually an annual interest rate. For daily compounding we need to divide the interest rate by 365. So,

The Future Value of an annuity formula is:

Substituting the values in the equation above we get,

------ (1)

The only value that comes closest to the value on the Left hand side of the equation is when the interest rate is 8.09%.

If annual interest rate is 8.09%, the daily interest rate is

Substituting this in the equation (1) we get,

Since 13335.18058 is closest to 13333.33333, 8.09% is the interest rate I must earn to achieve my goal of becoming a millionaire.

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