George is considering two different investment options. The first option offers 7.4% per year simple interest on the
initial deposit. The second option offers a 6.5% interest rate but is compounded quarterly. He may not withdraw any of
the money for three years after the initial deposit. Once the minimum 3 years is reached, he can choose to withdraw his
money or continue to collect interest. Suppose that George opens one of each type of account and deposits $10,000
into each.
Part A: Determine the value of the simple interest investment at the end of three years. Use the formula
A = P + Prt, where A represents the value of the investment, P represents the original amount, r represents the
rate, and t represents the time in years. Show your work.
Part B: Determine the value of the compound-interest investment at the end of three years. Use the formula
A = P(1+) , where A represents the value of the investment, P represents the original amount, r represents
the rate compounded n times per year, and t represents the time in years.
Show your work.
Part : Which investment is better over the first three years?
Explain your answer by using your work from Parts A and B as support.
Part D: How would you advise George to invest his money if he is unsure how long he will keep the money in the
account? Justify your reasoning using a graph or table.

Part A: The value of the simple interest investment at the end of three years is $12,220

Part B: The value of the compounded quarterly interest investment at the end of three years is $12,134.08

Part C: The simple interest investment is better over the first three years

Part D: I advise George to invest his money in the compounded interest investment if he will keep the money for a long time

Step-by-step explanation:

Part A:

A = P + P r t, where

A represents the value of the investmentP represents the original amountr represents the  rate in decimalt represents the time in years

∵ George deposits $10,000

∴ P = 10,000

∵ First option offers 7.4% per year simple interest

∴ r = 7.4% = 7.4 ÷ 100 = 0.074

∵ He may not withdraw any of  the money for three years after

   the initial deposit

∴ t = 3

- Substitute all of these values in the formula above

∴ A = 10,000 + 10,000(0.074)(3)

∴ A = 10,000 + 2,220

∴ A = 12,220

The value of the simple interest investment at the end of three years is $12,220

Part B:

, where

A represents the value of the investmentP represents the original amountr represents the  rate in decimaln is a number of periods of a yeart represents the time in years

∵ George deposits $10,000

∴ P = 10,000

∵ The second option offers a 6.5% interest rate compounded quarterly

∴ r = 6.5% = 6.5 ÷ 100 = 0.065

∴ n = 4 ⇒ quarterly

∵ He may not withdraw any of  the money for three years after

   the initial deposit

∴ t = 3

- Substitute all of these values in the formula above

∴

∴

∴ A = 12,134.08

The value of the compounded quarterly interest investment at the end of three years is $12,134.08

Part C:

∵ 12,220 > 12,134.08

∴ The simplest interest investment is better than the compounded

    interest investment at the end of three years

The simple interest investment is better over the first three years

Part D:

I advise George to invest his money in the compounded interest investment if he will keep the money for a long time

Look to the attached graph below

The red line represents the simple interest investmentThe blue curve represents the compounded interest investment(Each 1 unit in the vertical axis represents $1000)After 0 years and before 4.179 years the red line is over the blue curve, that means the simple interest is better because it gives more money than the compounded interestAfter that the blue curve is over the red line that means the compounded quarterly is better because it gives more money than the simple interest

/-/////////looks tough ‍♂️

The answer is d, none of above hope i