Answer:
Step-by-step explanation:
To calculate the required values, we can use the formulas and tables for future value of $1, present value of $1, future value annuity of $1, and present value annuity of $1. Here are the step-by-step calculations:
Given data:
Principal amount (P) = $5,800
Interest rate (r) = 10% or 0.10
Time period (n) = 4 years
Calculate the balance in the savings account at the end of 4 years (future value of $1):
Future Value (FV) = P * (1 + r)^n
FV = $5,800 * (1 + 0.10)^4
FV = $5,800 * 1.4641
FV ≈ $8,499.80
So, the balance in the savings account at the end of 4 years will be approximately $8,499.80.
Calculate the total interest earned over the 4 years:
Total Interest = Future Value - Principal Amount
Total Interest = $8,499.80 - $5,800
Total Interest ≈ $2,699.80
The total interest earned over the 4 years will be approximately $2,699.80.
Calculate the interest revenue earned in 2021 and 2022:
To calculate interest revenue for each year, we need to find the increase in the account balance from the previous year. The interest earned in 2021 will be the balance at the end of 2021 minus the initial deposit. The interest earned in 2022 will be the balance at the end of 2022 minus the balance at the end of 2021.
Interest Revenue in 2021 = Balance at the end of 2021 - Initial Deposit
Interest Revenue in 2022 = Balance at the end of 2022 - Balance at the end of 2021
Let's calculate:
Interest Revenue in 2021:
FV at the end of 2021 = $5,800 * (1 + 0.10)^1 ≈ $6,380
Interest Revenue in 2021 = $6,380 - $5,800 ≈ $580
Interest Revenue in 2022:
FV at the end of 2022 = $5,800 * (1 + 0.10)^2 ≈ $7,018
Interest Revenue in 2022 = $7,018 - $6,380 ≈ $638
So, the interest revenue earned in 2021 is approximately $580, and in 2022, it is approximately $638.