Answer
Find out the how much money must be deposited today to become $1450 in 50 years at 4.5% compounded continuously .
To prove
Formula
[tex]Compound\ interest = Principle (1 + rate)^{time}[/tex]
Where rate is in the decimal form
As given
$1450 in 50 years at 4.5% compounded continuously.
Put all the values in the formula
Rate in the decimal form.
[tex]= \frac{4.5}{100}[/tex]
= 0.045
Compound interest = $1450
[tex]1450 = Principle(1 + 0.045)^{50}[/tex]
[tex]1450 = Principle (1.045)^{50}[/tex]
[tex]1450 = Principle (1.045)^{50}[/tex]
[tex]principle = \frac{1450}{9.03}[/tex]
Principle= $ 160.58 (approx)
As 1 dollar = 100 cent
Now convert amount into the cent .
Principle= 160.58 × 100 cent
= 16058 cent
Therefore the amount deposit in the account is 16058 cent.
