Math

QuestionWhat initial deposit is required to reach \5,000in14yearswith5,000 in 14 years with 8\%$ simple interest?

Studdy Solution

STEP 1

Assumptions1. The final amount in the account should be $5,000. The account earns8% simple interest annually3. The time period is14 years4. The interest is not compounded, it's simple interest

STEP 2

We will use the formula for simple interest to solve this problem. The formula for simple interest isA=(1+rt)A =(1 + rt)Where- A is the amount of money accumulated after n years, including interest. - is the principal amount (the initial amount of money). - r is the annual interest rate (in decimal form). - t is the time the money is invested for, in years.

STEP 3

We know the final amount A, the interest rate r, and the time t. We need to find the principal amount. So, we rearrange the formula to solve for=A1+rt = \frac{A}{1 + rt}

STEP 4

Now, plug in the given values for A, r, and t to calculate.
=$,0001+0.08×14 = \frac{\$,000}{1 +0.08 \times14}

STEP 5

Before we calculate, let's simplify the denominator.
1+0.08×14=2.121 +0.08 \times14 =2.12So, the equation becomes=$5,0002.12 = \frac{\$5,000}{2.12}

STEP 6

Now, calculate.
=$5,0002.12=$2,358.49 = \frac{\$5,000}{2.12} = \$2,358.49So, you would need to deposit approximately 2,358.49intheaccountnowinordertohave2,358.49 in the account now in order to have 5,000 in the account in14 years.

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