You plan to retire in 30 years and would like to have $1,000,000 in investments. How much money would you have to invest today at a 7% annual interest rate compounded daily to reach your goal in 30 years? (Assume all years have 365 days. Round your answer to the nearest cent.)

$4,739.34

Explanation:

Step one :

Given data

final amount $1,000,000

initial principal balance??

annual interest rate=7%

time (in years)=30 years

Step two:

Applying the

Simple interest Formula

A = P (1 + rt)

A=final amount

P=initial principal balance?

Let us set this as x

r=annual interest rate

t=time (in years)

Step three :

Plugin our data into the formula We have

1,000,000=x(1+7*30)

1,000,000=x(1+210)

1,000,000=x(211)

Opening bracket we have

1,000,000=211x

Divide both sides by 211 we have

1,000,000/211=x

$4,739.34

Hence the money you have to invest today at a 7% annual interest rate compounded daily to reach your goal in 30 years

Is $4,739.34

Use the compound interest formula.

Let A = the ending amount

Let P = the principal

Let r = the interest rate

Let n = the amount compounded a year

Let t = time

A = P(1 + r/n) ^(n/t)

Substitute your numbers in

1,000,000 = P(1 + .07/365)^(365/30). Divide each side by (1 + .07/365)^(365/30).

365 / 30 = 10,950

1,000,000/(1 + .07/365)^(10,950) = P. Calculate your value for P.

$122,481.09 = P

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2 5/8 is the final answer! : )