Question

You invested $2,000 in a 15 year CD at the age of 15. The account pays 3% interest compounded continuously. How much money will you have after 15 years? (Round to the nearest cent.)

Answer 1

To calculate the future value of a $2,000 investment with 3% interest compounded continuously for 15 years, use the formula A = Pe^(rt), giving you approximately $3141.40 after 15 years.

Step-by-step explanation:

Calculating Compound Interest for Investment Gains

If you invested $2,000 in a 15-year CD at an interest rate of 3% compounded continuously, you can calculate the future value of this investment using the formula for continuous compounding, which is A = Pert, where P is the principal amount, e is the base of the natural logarithm (approximately 2.71828), r is the annual interest rate as a decimal, and t is the time in years. Plugging in the values, you get:

A = 2000 × e(0.03 × 15)

Calculating this expression:

A = 2000 × e0.45 ≈ $2000 × 1.5707 ≈ $3141.40

Therefore, after 15 years, you will have approximately $3141.40 in your CD account.