Question

To save for the purchase of a new car, a deposit was made into an account that earns 8% annual simple interest. Another deposit, $1700 less than the first deposit, was placed in a certificate of deposit (CD) earning 12% annual simple interest. The total interest earned on both accounts for 1 year was $676. How much money was deposited in the CD?
$

Answer 1

The amount deposited in CD is $660

Solution:

Given that , To save for the purchase of a new car, a deposit was made into an account that earns 8% annual simple interest.  

Let the amount deposited in new car be $ n

Another deposit, $1700 less than the first deposit, was placed in a certificate of deposit (CD) earning 12% annual simple interest.  

Then, amount deposited in CD will be $ (n – 1700)

The total interest earned on both accounts for 1 year was $676

The simple interest is given as:

$\text { Simple interest }=\frac{\text { principal } \times \text {rate} \times \text {time}}{100}$

Simple interest for purchase of new car:

$\text { S. } \mathrm{I}=\frac{n \times 8 \times 1}{100}=\frac{8 n}{100}$

Simple interest for CD:

$\text { S.I } =\frac{(n-1700) \times 12 \times 1}{100}=\frac{12(n-1700)}{100}$

Now, given that S.I for new car + S.I for CD = 676

$\begin{array}{l}{\frac{8 n}{100}+\frac{12(n-1700)}{100}=676} \\\\ {\frac{8 n+12 n-12 \times 1700}{100}=676}\end{array}$

20n = 67600 – 20400

n = 2360

So money deposited in CD = n - 1700 = 2360 – 1700 = 660

Hence, the CD deposit amount is $660