You have invested $5,000 into a certificate of deposit for 5 years. it pays a 6% annual nominal rate, compounded semiannually. what is the value of the certificate of deposit at the end of 5 years?

The formula for calculating the ending balance of the certificate of deposit is

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

Where:

P = initial deposit amount

r = annual nominal interest rate

t = number of years

n = number of compounding periods per year (for example, 12 for monthly compounding)

A = ending balance

So in the problem:

P = $5,000

r = 0.06 or 6%

n = 2 since it is semi-annual.

t = 5 years

Solution:

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

= 5000 x (1 + 0.06/2) ^2 (5)

= 5000 x (1.03) ^10

= 5000 x 1.343916379

= $6,719.58 is the value of the certificate after 5 years.