Final answer:
To find the total balance in Mark's savings account after 5 years with an annual interest rate of 7%, we apply the compound interest formula A = P(1 + r)^t. By plugging in the initial balance of $29,820 and compounding annually for 5 years, we can calculate the future balance.
Step-by-step explanation:
The question at hand involves calculating the future balance of a savings account that accrues compound interest. Mark's initial balance is $29,820, and it earns 7% interest per year. To find the total balance after 5 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
- A = the amount of money accumulated after n years, including interest.
- P = the principal amount (the initial amount of money).
- r = the annual interest rate (decimal).
- n = the number of times that interest is compounded per year.
- t = the time in years.
In Mark's case, the interest is compounded once per year (n=1), so the formula simplifies to:
A = P(1 + r)^t
Plugging in Mark's values gives us:
A = 29,820(1 + 0.07)^5 = 29,820(1.07)^5
After calculating the value of (1.07)^5 and multiplying by 29,820, we would obtain Mark's total balance after 5 years.