Mia Kaminsky wants to attend Riverside Community College. She will need to have $25,000 six years from today. Mia is wondering what she will have to put back in the bank today so she will have $25,000 six years hence. Her bank pays 5 percent compounded semiannually.

Question

mathstudent55 · Answer

F = P(1 + i)^n
F = Future value = $25,000
P = Present value = unknown
i = 5% compounded semiannually; This means 5/100/2 per compounding period
n = number of compounding periods = 12 (2 periods per year for 6 years)

25,000 = P(1 + 5/100/2)^12
You are solving for P
25,000 = P(1 + 0.025)^12
25,000 = P(1.025)^12
25,000 = P(1.34489)
P = 25,000/1.34489
P = 18,588.88

Answer: $18,588.88

anonymous · Answer

What about the 5%?

mathstudent55 · Answer

In the formula, i is the interest rate, but it has to be expressed as a decimal per compounding period.
5% as a decimal is 5/100 = 0.05, but this is per year
Since the compounding is semiannual, that means twice a year, and the interest has to be expressed as how much it is in a compounding period, then is it 0.05/2 = 0.025.
By writing 5/100/2, I wrote the interest in decdimal and per compounding period in one step.