Question

How much money must be deposited today to become $1450 in 50 years at 4.5% compounded continuously. Round to the nearest cent if needed

Answer 1

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

$Compound\ interest = Principle (1 + rate)^{time}$

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.

$= \frac{4.5}{100}$

= 0.045

Compound interest = $1450

$1450 = Principle(1 + 0.045)^{50}$

$1450 = Principle (1.045)^{50}$

$1450 = Principle (1.045)^{50}$

$principle = \frac{1450}{9.03}$

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.