Question

George is considering two different investment options. The first option offers 7.4% per year simple interest on the

Answer 1

Answer:

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 investment
• P represents the original amount
• r represents the  rate in decimal
• t 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:

$A=P(1+\frac{r}{n})^{nt}$, where

• A represents the value of the investment
• P represents the original amount
• r represents the  rate in decimal
• n is a number of periods of a year
• t 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

∴ $A=10,000(1+\frac{0.065}{4})^{(4)(3)}$

∴ $A=10,000(1.01625)^{12}$

∴ 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 investment
• The 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 interest
• After 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