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:
\(\[ \text{Simple Interest} = \text{Principal} \times \text{Interest Rate} \times \text{Time (in years)} \]\)
Principal = \($1500
Simple annual interest rate = 4% = 0.04
Time = 20 years
Using the formula for simple interest, we calculate the total interest earned over 20 years:
Total simple interest = $\)1500 \times 0.04 \times 20
Total simple interest = \($1500 \times 0.8
Total simple interest = $\)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 = \($1500 + $\)1200
Total value of Account A = \($2700
So, at the end of 20 years, Account A will be worth $\)2700.
2. Account B: Compound Interest Calculation
Account B pays 4% interest compounded annually. Compound interest is calculated using the formula:
\(\[ \text{Compound Interest} = \text{Principal} \times \left(1 + \text{Interest Rate}\right)^{\text{Number of times interest is compounded}} \]\)
Since interest is compounded annually, the number of times interest is compounded each year is 1.
Principal = \($1500
Annual compound interest rate = 4% = 0.04
Time = 20 years
Using the formula for compound interest, we calculate the total amount in Account B after 20 years:
Total value of Account B = $\)1500 \times (1 + 0.04)^{20}
Total value of Account B = \($1500 \times (1 + 0.04)^{20}
Total value of Account B = $\)1500 \times (1.04)^{20}
Now we need to calculate \(\( (1.04)^{20} \)\):
\(\( (1.04)^{20} \approx 2.191123 \)\) (rounded to six decimal places for precision)
Using this value in our formula:
Total value of Account B = \($1500 \times 2.191123
Total value of Account B = $\)3286.6845 (approximately)
Rounding to the nearest cent, we have:
Total value of Account B ≈ \($3286.68
So, at the end of 20 years, Account B will be worth approximately $\)3286.68.
To present both answers using dollars and cents:
At the end of 20 years:
- The total value of Account A will be \($2700.00
- The total value of Account B will be $\)3286.68
