Jabulani has managed to save $$ R 85,000 $$ from his salary. He wants this money to earn him income at the end of every year. He decides to invest all of his money with two different banks, FNB and ABSA, paying him $$ 6.5 \% $$ annually and $$ 8 \% $$ annually, respectively. How much should Jabulani invest with each bank if he wishes to get $$ R 5,000 $$ per year.

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UpStudy AI · Accepted Answer

Let 
$$
x = \text{amount invested with FNB (at } 6.5\% \text{)}
$$
and 
$$
y = \text{amount invested with ABSA (at } 8\% \text{)}.
$$
Since Jabulani invests all his money, we have
$$
x + y = 85000.
$$
The total annual interest is required to be R5000, so
$$
0.065x + 0.08y = 5000.
$$

Substitute 
$$
y = 85000 - x
$$
into the interest equation:
$$
0.065x + 0.08(85000 - x) = 5000.
$$
Distribute and simplify:
$$
0.065x + 6800 - 0.08x = 5000,
$$
$$
-0.015x + 6800 = 5000.
$$
Subtract 6800 from both sides:
$$
-0.015x = -1800.
$$
Divide by $$-0.015$$:
$$
x = \frac{-1800}{-0.015} = 120000.
$$

Then,
$$
y = 85000 - 120000 = -35000.
$$

A negative value for $$y$$ is not possible in this context. In fact, note that if Jabulani invested all his money in FNB (which pays the lower rate of $$6.5\%$$), the interest would be
$$
0.065 \times 85000 = 5525,
$$
which is already more than R5000. Therefore, there is no way to split R85000 between these two banks so that the total annual interest is exactly R5000.

The conclusion is that no solution exists under the given conditions.
Jabulani cannot invest his R85,000 in FNB and ABSA at the given interest rates to earn exactly R5,000 per year.

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