Video Transcript
If Jennifer invested 4,500 dollars in a
certificate of deposit for five years and earned 765 dollars, determine the rate of
interest.
In order to calculate the amount of
interest earned, we can use the formula 𝐼 equals 𝑃 multiplied by 𝑅 multiplied by 𝑇. 𝐼 is the amount of interest earned, 𝑃
is the principal amount. This is the amount invested. 𝑅 is the rate of interest written as a
decimal. And finally, 𝑇 is the amount of
time. In this question, we know that the amount
invested is 4,500 dollars. So, 𝑃 is equal to 4,500. The amount was deposited for five
years. Therefore, 𝑇 is equal to five. The amount of interest that Jennifer
earned was 765 dollars. So, this is the value of 𝐼. We’re trying to calculate the rate of
interest 𝑅.
Substituting these values into the
formula gives us 765 is equal to 4,500 multiplied by 𝑟 multiplied by five. As multiplication is commutative, we can
multiply 4,500 by five first. The equation simplifies to 765 is equal
to 22,500 multiplied by 𝑟. Dividing both sides of this equation by
22,500 gives us 𝑟 is equal to 0.034. To convert from a decimal to a
percentage, we multiply by 100. This moves all of the digits two places
to the left, and the interest rate is 3.4 percent. 4,500 dollars invested for five years at
3.4 percent simple interest per year would earn 765 dollars.
