5 Justin deposited [tex]$1500 into each of two savings accounts. Account A pays 4% annual simple interest. Account B pays 4% interest compounded annually Justin made no
additional deposits or withdrawals into either account
Calculate the value of Account A and the value of Account B at the end of 20 years. Present your answers using both dollars and cents.
At the end of 20 years, the total value of Account A will be $[/tex] 60,166.56
At the end of 20 years, the total value of Account B will be $



Answer :

Let's begin by breaking down the problem and solving each part systematically.

1. Account A: Simple Interest Calculation

Account A pays 4% annual simple interest. Simple interest is calculated using the formula:

[tex]\[ \text{Simple Interest} = \text{Principal} \times \text{Interest Rate} \times \text{Time (in years)} \][/tex]

Principal = [tex]$1500 Simple annual interest rate = 4% = 0.04 Time = 20 years Using the formula for simple interest, we calculate the total interest earned over 20 years: Total simple interest = $[/tex]1500 \times 0.04 \times 20
Total simple interest = [tex]$1500 \times 0.8 Total simple interest = $[/tex]1200

Now, we add the simple interest earned to the original principal to get the total value of Account A after 20 years:

Total value of Account A = Principal + Total simple interest
Total value of Account A = [tex]$1500 + $[/tex]1200
Total value of Account A = [tex]$2700 So, at the end of 20 years, Account A will be worth $[/tex]2700.

2. Account B: Compound Interest Calculation

Account B pays 4% interest compounded annually. Compound interest is calculated using the formula:

[tex]\[ \text{Compound Interest} = \text{Principal} \times \left(1 + \text{Interest Rate}\right)^{\text{Number of times interest is compounded}} \][/tex]

Since interest is compounded annually, the number of times interest is compounded each year is 1.

Principal = [tex]$1500 Annual compound interest rate = 4% = 0.04 Time = 20 years Using the formula for compound interest, we calculate the total amount in Account B after 20 years: Total value of Account B = $[/tex]1500 \times (1 + 0.04)^{20}
Total value of Account B = [tex]$1500 \times (1 + 0.04)^{20} Total value of Account B = $[/tex]1500 \times (1.04)^{20}

Now we need to calculate [tex]\( (1.04)^{20} \)[/tex]:

[tex]\( (1.04)^{20} \approx 2.191123 \)[/tex] (rounded to six decimal places for precision)

Using this value in our formula:

Total value of Account B = [tex]$1500 \times 2.191123 Total value of Account B = $[/tex]3286.6845 (approximately)

Rounding to the nearest cent, we have:

Total value of Account B ≈ [tex]$3286.68 So, at the end of 20 years, Account B will be worth approximately $[/tex]3286.68.

To present both answers using dollars and cents:

At the end of 20 years:
- The total value of Account A will be [tex]$2700.00 - The total value of Account B will be $[/tex]3286.68