Question

A person places $290 in an investment account earning an annual rate of 2.2%, compounded continuously. Using the formula V = P e r t V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 18 years.

Answer 1

Answer: $430.90

Explanation:

Given formula :
`V = P e^( r t)`, where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest.

Given: P= $290 , r=2.2% = 0.022 [divide percent by 100 to remove percent sign '%']

Also, t=18 years

Now,
`V=290e^(0.022*18)=290e^(0.396)`

`=290*1.48586931755\approx\$430.90`

Hence, the amount of money in the account after 18 years. = $430.90