Jamal is planning to invest up to $24,000 in City Bank or State Bank. He wants to invest at least $3,000 in City Bank but not more than $11,000. Since State Bank does not insure more than $18,000, he wants to invest no more than this amount in State Bank. The interest at City Bank is 6%, and the interest at State Bank is 11%.
How much should he invest in each bank to earn the most interest?
Answer (2)
$24,000 ---------> City or State Bank $3,000 < City Bank < $11000 State Bank< $18,000 City Bank = .06 of interest State Bank = .11 of interest
Bold = Answer
State Bank - (18, 000)(.11)-----> $1980 ** } Total Interest = **City Bank - (6000)(.06)---------->"> 2 , 430 ∗ ∗ < / u >< u > ∗ ∗ C i t y B ank − ( 6000 ) ( .06 ) − − − − − − − − − − > 360 **
State Bank - (13000)(.11) ----------> $1,430 } Total Interest = $2,090 City Bank - (11000)(.06) -------------> $660
State Bank- (17000)(.11) ---------->$ 1870 } Total Interest = "> 2 , 290 C i t y B ank − ( 7000 ) ( .06 ) − − − − − − − − − − − − − − − − > 420
To maximize interest, Jamal should invest $6000 in City Bank and $18000 in State Bank, which yields a total interest of $2340. This satisfies all investment constraints. Thus, it is the optimal choice for his investment strategy.
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