Question

Danica is saving money to go on a trip to Europe after her

college graduation. She will finish college six years from now.
If the certificate of deposit that she buys now pays 8% interest
compounded continuously, how much should she invest now
to have $3000 for the trip? Use A = Pe where P = principal,

Answer 1

Danica should invest approximately $1855.67 now to have $3000 in six years if her investment yields an 8% interest rate compounded continuously. The future value formula with continuous compounding, A = Pert, is utilized to calculate the present value that needs to be invested.

Step-by-step explanation:

The question asks how much Danica should invest now to have $3000 for a trip to Europe in six years, with an 8% interest rate compounded continuously. To solve this, we use the formula for continuous compounding: A = Pert, where A is the future value, P is the principal amount (initial investment), r is the annual interest rate (expressed as a decimal), t is the time in years, and e is Euler's number (approximately 2.71828).

Given that A = $3000, r = 0.08, and t = 6, we need to find P. Rearranging the formula to solve for P gives us P = A / (ert). Plugging in the values, we calculate P as follows:

P = 3000 / (e(0.08 × 6))

P = 3000 / (e0.48)

P = 3000 / (e0.48) ≈ 3000 / 1.617

P ≈ $1855.67

Therefore, Danica should invest approximately $1855.67 now to have $3000 in six years with an 8% continuous compounding interest rate.