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effort
Senior Member

USA
38 Posts

 Posted - 03/20/2013 :  13:10:27 If \$2000.00 is invested at 3% interest compounded every four months, what will be the amount in the investment after 10 years? I use the formula A = P(1 + (r/n))raised to the ntA= 2000(1+(.03/3))raised to (310)So A = 2000(1.01)raised to 30 which equals \$2696.70My first question is why can't I solve it by 2000(1 + .03) raised to the 30? Why do I need the rate divided by 3 for the top answer of 2696.70? Working the problem as 2000(1 + .03)raised to the 30 yields \$4854.5 which isn't the same amount as using the above formula which yielded \$2696.70My third question is why if I use 2000(1.03) and get the total and then do it again til I have done it 30 times.....why doesn't it equal to 2696.70 if I am just adding the amounts of up?Since posting this problem, I have kept thinking about it. Does the difference in the answers have anything to do with the interest rate being compounded? Is the problem saying that 3% is the total year interest rate? If so, I am assuming this would mean that you would have to divided the interest rate by 4 to get the actual rate for each four months? I'm not sure about my reason so any help on this is appreciated. Edited by - effort on 03/20/2013 15:07:05

Ultraglide

299 Posts

 Posted - 03/20/2013 :  16:48:09 When the interest rate is quoted, i.e. 3%, that is the annual rate so in this case you want the interest per period which is 1% (3%/3). Since it is calculated 3 times per year, there are 30 (3x10) interest conversion periods. Hence your original calculation is correct.

the_hill1962

USA
1469 Posts

 Posted - 03/22/2013 :  11:06:38 You have a typo in your answer. It is \$2695.70, not \$2696.70

TchrWill

USA
80 Posts