Question

A person places $79700 in an investment account earning an annual rate of 1%, compounded continuously. Using the formula V, equals, P, e, start superscript, r, t, end superscriptV=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 2 years.

Answer 1

Using the formula for continuous compounding, the future value of a $79,700 investment at an annual rate of 1% for 2 years is $81,349.44.

Step-by-step explanation:

To find the amount of money in an investment account after 2 years with continuous compounding, we use the formula V = Pert, (where V is the future value of the investment, P is the principal amount, e is the base of the natural logarithm, r is the annual interest rate (as a decimal), and t is the time in years).

In this example, an initial investment of $79,700 is placed in an account with an annual interest rate of 1%, compounded continuously, for 2 years.

Plugging the values into the formula gives us the following calculation:

V = 79700 * e0.01*2

= 79700 * e0.02

= 79700 * 1.0202013400267558 (using a calculator for e0.02)

= $81349.44 (rounded to the nearest cent)

The amount of money in the account after 2 years, to the nearest cent, is $81,349.44.