Martina deposited \$4000 into an account with 3% interest, compounded semiannually. Assuming that no withdrawals are made, how much will she have in the account after 7 years?

Do not round any intermediate computations, and round your answer to the nearest cent.

Relevance

... An = A0 (1 + r/2)^(2y) ← semiannually = 2 times per year

or An = 4000 (1 + .03/2)^(2*7)

or An = 4000 (1.015)^(14)

or An = \$ 4,927.02

• Anonymous

It depends. Is the 3% interest rate a 6 month interest rate? Or is it a one year interest rate? Interest is being compounded every 6 months, so we need to work in a 6 month interest rate.

If 3% is a 6 month interest rate....

The account will be credited with interest for 7 years, or 14 six month periods.

Future Value = 4000(1+i)^n = 4000(1.03)^14 = \$6050.36

If 3% is a one year interest rate... then it is a little trickier:

Using a 3% nominal annual rate, then we need to compute a six month interest rate.

Since a 6 month period is exactly one half of a year, the 6 month rate is exactly one half of 3% or 1.5%

Future Value = 4000(1+i)^n = 4000(1.015)^14 = \$4927.02

• Year 1 = 4000

Year 2 = 4120

Year 3 = 4243.6

Year 4 = 4370.91

Year 5 = 4502.04

Year 6 = 4637.01

Year 7 = 4776.21