Questions: Graduation is 5 years away and you want to have 1300 available for a trip. If your bank is offering a 5-year CD (certificate of deposit) paying 3.5% simple interest, how much do you need to put in this CD to have the money for your trip?

Graduation is 5 years away and you want to have 1300 available for a trip. If your bank is offering a 5-year CD (certificate of deposit) paying 3.5% simple interest, how much do you need to put in this CD to have the money for your trip?

Transcript text: Homework: Simple and Comp Start With Hello: Creating Ki rses/662433/assignments/14990298?module_item_id=48059798 Homework: Simple and Compound Interest Score: $15 / 52$ Answered: $6 / 20$ Progres: Question 7 Graduation is 5 years away and you want to have $\$ 1300$ available for a trip. If your bank is offering a 5 -year CD (certificate of deposit) paying $3.5 \%$ simple interest, how much do you need to put in this $C D$ to have the money for your trip? \$ $\square$ Question Help: Video Message instructor Post to forum Submit Question

Solution

Solution Steps

Step 1: Convert the Interest Rate

First, convert the interest rate from a percentage to a decimal by dividing by 100. Interest Rate (decimal) = 3.5 / 100 = 0.035

Step 2: Use the Simple Interest Formula

The formula for future value using simple interest is $FV = P(1 + rt)$, where $FV$ is the future value, $P$ is the principal amount (initial deposit), $r$ is the annual interest rate in decimal form, and $t$ is the time in years.

Step 3: Rearrange the Formula to Solve for the Initial Deposit (P)

To find the initial deposit, we rearrange the formula to $P = \frac{FV}{(1 + rt)}$.

Step 4: Calculate the Initial Deposit

Plugging in the values of $FV$ = 1300, $r$ = 0.035, and $t$ = 5, we calculate the initial deposit as $P = \frac{1300}{(1 + 0.035 \times 5)} = 1106.38$.