Question

Suppose you take $25,000 and deposit some of it into a savings account that pays 2.2% interest. You then take the rest of the money and deposit it in a CD that pays 3.05% interest at the end of 10 years the value of both accounts is $31,648. How much was deposited into each account?

Answer 1

The amount deposited in the savings account is $11,494.12

The amount deposited in the CD account is $13,505.88

Explanation:

Firstly, let’s calculate the amount of interest;

Interest = Amount at end of 10 years - amount deposited= 31,648 -25,000 = 6,648

Let the amount deposited in the savings account be $x while the amount deposited in the CD account be $y

Mathematically;

x + y = 25,000 ••••••••••(i)

Now the formula for simple interest is;

PRT/100

where P is the amount deposited, r is the rate and T is the time

On the savings account, amount of interest generated will be;

(x * 2.2 * 10)/100 = 22x/100

On the CD act, amount of interest generated will be;

(y * 3.05 * 10)/100 = 30.5y/100

The addition of both give the total interest;

22x/100 + 30.5y/100 = 6648

Multiply through by 100

22x + 30.5y = 664800 •••••••(ii)

From i, x = 25,000 - y

Substitute this into ii

22(25000-y) + 30.5y = 664800

550,000 -22y + 30.5y = 664,800

8.5y = 664,800-550,000

8.5y = 114,800

y = 114,800/8.5

y = $13,505.88

x = 25,000 -y

x = 25,000 - 13,505.88

x = $11,494.12