Second National Bank computes interest semiannually.If the annualized interest rate (APR)is currently 6 percent,the amount deposited today should be multiplied by which future value factor to calculate the amount that will accumulate by the end of 10 years?
A)20 periods at 12 percent
B)20 periods at 3 percent
C)10 periods at 6 percent
D)10 periods at 3 percent

Question

Quizplus · Accepted Answer

Since the interest is computed semiannually, there will be a total of 20 semiannual periods over 10 years. Using the formula for future value with semiannual compounding:

FV = PV x (1 + r/n)^(nt)

Where PV is the present value (amount deposited today), r is the annual interest rate (APR), n is the number of compounding periods in a year (2 for semiannual), and t is the number of years.

For this problem, we have:

PV x (1 + 0.06/2)^(2x10) = FV

Simplifying:

PV x 1.0618^20 = FV

The future value factor for 20 semiannual periods at 3% (half of the annual 6% rate) is 1.0618^20. Therefore, the answer is B.

Second National Bank Computes Interest Semiannually