2410.12 – Spend or Save?

Sue was given a chunk of money for graduation from a distant aunt she’d not even known she had. Her first thought was Spend. Then she decided she really ought to Save it. She has divided the money into two parts. One of these is $250 more than the other. The smaller part is now invested at 6% interest and the larger part at 8%. A year later the total interest she has accumulated is $72.50. How much money was she given in the first place?

Solution

Call the two parts xx and x+250x + 250. Then 0.06x+0.08(x+250)=72.50.06 x + 0.08 (x + 250) = 72.5. Therefore,

0.06x+0.08x+20=72.50.14x=52.5x=$375\begin{align*}0.06 x + 0.08 x + 20 &= 72.5 \\0.14x &= 52.5 \\x &= \$375\end{align*}

The total gift was

x+(x+$250)=$375+$625=$1000\begin{align*}x + (x + \$250) &= \$375 + \$625 \\&= \$1000\end{align*}

We should all be so lucky.