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.
