Question

Three different accounts are described below.order the accounts according to their values after 10 years ,from greatest to least

Answer 1

Answer:

3.You deposit $1000 in an account that earns 9% annual interest compounded semiannually.

1. You deposit $950 in an account that earns 9% annual interest compounded daily.

2. You deposit $1000 in an account that earns 8% annual interest compounded daily.

4. You deposit $1000 in an account that earns 10% simple interest.

Step-by-step explanation:

P.S - The exact question is -

To find - Three different accounts are described below. Order the accounts  

             according to their values after 10 years, from greatest to least.

             1. You deposit $950 in an account that earns 9% annual

                 interest compounded daily.

            2. You deposit $1000 in an account that earns 8% annual

                 interest compounded daily.

             3.You deposit $1000 in an account that earns 9% annual

                 interest compounded semiannually.

              4. You deposit $1000 in an account that earns 10% simple interest.

Proof -

1.)

Value after 10 years = 950( 1 + 0.09)¹⁰

                                 = 950 ( 1.09)¹⁰

                                 = 950(2.37) = 2248.995

⇒Value after 10 years = 2248.995

2.)

Value after 10 years = 1000( 1 + 0.08)¹⁰

                                 = 1000 ( 1.08)¹⁰

                                 = 1000(2.159) = 2158.925

⇒Value after 10 years = 2158.925

3.)

As it is compounded semiannually , so time period is doubles and rate goes half.

Value after 10 years = 1000( 1 + 0.045)²⁽¹⁰⁾

                                 = 1000 ( 1.045)²⁰

                                 = 1000(2.412) = 2411.714

⇒Value after 10 years = 2411.714

4.)

Value after 10 years = 1000×$\frac{10}{100}$×10 = 1000

∴ we get

2411.714 > 2248.995 > 2158.925 > 1000

⇒ 3.) > 1.) > 2.) > 4.)

So,

3.You deposit $1000 in an account that earns 9% annual interest compounded semiannually.

1. You deposit $950 in an account that earns 9% annual interest compounded daily.

2. You deposit $1000 in an account that earns 8% annual interest compounded daily.

4. You deposit $1000 in an account that earns 10% simple interest.