Asked by Adrian Montoya on Jun 17, 2024
Verified
Loretta deposits $350 every quarter into a savings account that earns 4.5% interest compounded quarterly.What is the balance after 7 years?
A) $10,312.63
B) $11,344.18
C) $11,444.27
D) $12,477.74
Compounded Quarterly
Describes the process of adding interest to the principal sum of a deposit or loan, with this addition of interest occurring four times a year.
Quarterly
Occurring every three months or four times a year, often used in reference to financial reports or payments.
Interest Rate
The proportion of a loan or savings amount paid as interest to the lender or paid to the saver, usually expressed as an annual percentage.
- Estimate anticipated savings using a range of compounding intervals.
- Calculate the future value of regular deposits into savings accounts.
Verified Answer
BB
Birva BarotJun 20, 2024
Final Answer :
C
Explanation :
First, we need to figure out the total number of periods over the 7 years. Since Loretta deposits every quarter, there are 4 periods in a year. Thus, there are 4 x 7 = 28 periods total.
Next, we can use the formula for compound interest to determine the balance after 7 years:
A = P(1 + r/n)^(nt)
where:
A = final amount
P = principal (initial deposit)
r = annual interest rate (4.5%)
n = number of times interest is compounded per year (4)
t = time in years (7)
Plugging in the values, we get:
A = 350(1 + 0.045/4)^(4*7)
A ≈ $11,444.27
Therefore, the best choice is C, which matches our calculated answer.
Next, we can use the formula for compound interest to determine the balance after 7 years:
A = P(1 + r/n)^(nt)
where:
A = final amount
P = principal (initial deposit)
r = annual interest rate (4.5%)
n = number of times interest is compounded per year (4)
t = time in years (7)
Plugging in the values, we get:
A = 350(1 + 0.045/4)^(4*7)
A ≈ $11,444.27
Therefore, the best choice is C, which matches our calculated answer.
Learning Objectives
- Estimate anticipated savings using a range of compounding intervals.
- Calculate the future value of regular deposits into savings accounts.