Question

Open-Ended You invest $1,000 in each of two accounts. Account A earns simple interest at a rateof 2.42% over 4 years. Account B earns simple interest at a rate of 2.42% over 24 months. Find theinterest earned by each account. How does the interest earned by the two accounts compare?Use paper and pencil. Give an example of two principal amounts and two simple interest rates thatwould earn equal amounts of interest in one year. Give an example of two principal amounts andtwo periods of time for which the simple interest earned at 2.76% would be equal.Account A earns $ after 4 years.(Simplify your answer. Type an integer or a decimal.)

Answer 1

Account A:

Initial Deposit 1000

2.42% for 4 years

Account B:

Initial Deposit 1000

2.42% in 24 months

We have to find the simple interest earned in each account. The formula for simple interest is:

`i=\text{Prt}`

Where

i is the interest earned

P is the initial amount

r is the rate of interest, in decimal

t is the tiem

For account A:

P = 1000

r = 2.42% = 0.0242

t = 4 years

Thus, the interest earned is:

`\begin{gathered} i=\text{Prt} \\ i=1000*0.0242*4 \\ i=96.8 \end{gathered}`

For account B:

P = 1000

r = 0.0242

t = 24 months = 24/12 = 2 years

Thus, the interest earned is:

`\begin{gathered} i=\text{Prt} \\ i=1000*0.0242*2 \\ i=48.4 \end{gathered}`

example:

i = Prt

Since we want an example where interest amount is same in a a year, we know i and t are constant. We just need to figure out two P's and two r's that give the same value.

Suppose the initial deposit is 2000 and the rate of interest is 5%.

Now, suppose intial deposit is 500 and rate of interest is 20%.

They would both equate the same interest in 1 year.