Question

Susan invests 2 times as much money at 6 % as she does at 5 %. If her total interest after 1 year is $510, howmuch does she have invested at each rate?Susan invests $___at 5% and $___ at 6%.

Answer 1

The interest formula is :

$I=Prt$

where I = interest

P = Principal amount

r = interest rate

t = time in years

From the problem, Susan invested twice the amount at 6% as she does at 5%.

If she invested P to 5%, the amount she invested to 6% will be 2P

Using the formula to calculate the two interests.

For 5% :

$\begin{gathered} I=P(0.05)(1) \\ I=0.05P \end{gathered}$

For 6% :

$\begin{gathered} I=2P(0.06)(1) \\ I=0.12P \end{gathered}$

The sum of the interests is $510

This will be :

$\begin{gathered} 0.05P+0.12P=510 \\ \text{Solve for P :} \\ 0.17P=510 \\ P=\frac{510}{0.17}=3000 \end{gathered}$

She invested $3000 for 5% and $6000 for 6%

The answers are :

5% : $3000

6% : $6000