Ivan has $8500 to invest. He will invest some of it in a long-term IRA paying 4% simple interest and the rest in a short-term CD earning 2.5% simple interest. After 1 year, Ivan's investments have earned $250 in interest. How much did Ivan invest in each account?

Question

Ivan has $8500 to invest. He will invest some of it in a long-term IRA paying 4% simple interest and the rest in a short-term CD earning 2.5% simple interest. After 1 year, Ivan&#039;s investments have earned $250 in interest. How much did Ivan invest in each account?

Rose Holmes · Accepted Answer

Let the amounts invested by Ivan in long term IRA earning 4 % simple interest and the short term CD earning 2.5 % simple interest be $ x and $ ( 8500- x) respectively.The interest on $ x at 4 % simple interest for 1 year is             x      ⋅      4        100    =      x    25  .The interest on 8500 -x at 2.5 % simple interest for 1 year is   (  8500  −  x  )  ⋅      2.5    100    =  8500  ⋅      2.5    100    −  2.5      x    100    =  212.5  −      x    40  .Then, since the total interest earned in 1 year is $ 250, we have       x    25    +  212.5  −      x    40    =  250 or,       x    25    −      x    40    =  250  −  212.5 or,             8      x      −      5      x        200    =  37.5 or,             3      x        200    =  37.5 or,   3  x  =  37.5  ⋅  200 or, 3x = 7500 so that   x  =      7500    3    =  2500. Then 8500 -x = 8500 -7500 = 1000. Thus, Ivan invested $ 7500 in  long term IRA earning 4 % simple intere and $ 1000 in the short term CD earning 2.5 % simple interest .

Ivan has $8500 to invest. He will invest some of it in a long-term IRA paying 4% simple interest and the rest in a short-term CD earning 2.5% simple interest. After 1 year, Ivan's investments have earned $250 in interest. How much did Ivan invest in each account?

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