After graduation in 2 years, Antwone would like to take a much needed vacation to the Caribbean Islands. He anticipates that the all inclusive vacation package will cost him $3,800. His bank will pay 3% per year compounded semiannually. How much does he need to deposit into this account each semiannual period, so that he can take his vacation in 2 years

Answer: $3,580.30 (converted to 2decimal places).

Antwone need to deposit " $3,580.30008" into the account each semi-annual period in order to take his vacation in 2 years

Explanation:

By using compound interest formula below to solve the question

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

A = amount (future value) = $3,800

P = principal (present value) ?

r = annual nominal rate = 3% = 0.03

n = today number of compounding years = semiannually (2 interest payments period in a year) = 2

t = time in years = 2

3,800 = p (1 + 0.03/2) ^2 (2)

3,800 = p (1 + 0.015) ^4

3,800 = p (1.015) ^4

3,800 = 1.06136355 p

divide both sides by 1.06136355

p = 3,800 / 1.06136355

p = $3,580.30008

≈$3,580.30 (rounded off to 2d. p)