Question

Suppose you have $2,000 and plan to purchase a 10-year certificate of deposit (CD) that pays 6.5% interest, compounded annually. How much will you have when the CD matures?

Answer 1

The value of the CD when it matures after 10 years will be approximately $3,795.86.

Step-by-step explanation:

To calculate the value of the CD at the end of 10 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the value of the CD at the end of the 10 years

P = the principal amount (initial investment) which is $2,000

r = the annual interest rate as a decimal, which is 6.5% expressed as 0.065

n = the compound frequency per year, which is 1 as the interest is compounded annually

t = the number of years, which is 10

Substituting the given values into the formula:

A = $2,000(1 + 0.065/1)^(1*10)

A = $2,000(1 + 0.065)^10

Using a calculator, we can evaluate the expression and find that A ≈ $3,795.856.

Therefore, the value of the CD when it matures after 10 years will be approximately $3,795.86.