1.) Convert the stated rate to an annual compound rate
0.034 / 12 = 0.0028333
(1.0028333^12) - 1 = 0.034534, or about 3.453%
2.) convert this to a "stated rate" for 24 periods per year...
[1.034534^(1/24)] - 1 = 0.00141566 < this is the stated rate that, when compounded over 24 periods, gives you the same annual compound rate as compounding monthly (as in #1)
Another way to look at this is (probably a simpler way): What semi-monthly rate, when compounded, gives you the equivalent of the monthly stated rate?
monthly stated rate: 0.034 / 12 = 0.0028333
the semi monthly stated rate, that when compounded for 2 periods gives you the monthly state rate:
[1.002833^(1/2)] - 1 = 0.00141566
check math: [1.0014566^2] - 1 = 0.0028333
3) use the semi-monthly stated rate you've calculated (in #2 or just above) in the FV ordinary annuity formula...
FVoa = PMT [((1 + i)^n - 1) / i]
n = 24 * 5 = 120
= 200[(1.00141566^120) - 1) / 0.00141566]
= 200[130.694766]]
= $26,138.95
I hope I explained this well enough for you to understand it.
When you invest twice $200/ Bank will take only the minimum balance in the month for interest payment. So first month they may take 200 next month 600 + interest of first month. So the formula cannot be applied.
I would like to know where & by who do you get 3.4% interest ?
I know how to do future problems and I know you have to divide the interest by 12 because it's monthly and multiply the number of periods by 12. What is throwing me off is the $200 twice a month. I have never had a problem where I was asked to find the future value where someone invested money twice per month. If anyone could help me I would greatly appreciate it.
