Asked by Lanie Barnhill on Jul 21, 2024
Verified
Don opened a retirement account with an APR of 3.25% compounded monthly.He is planning to retire in 15 years.About how much will he have in the account when he retires if he deposits $750 a month?
A) $173,677.27
B) $165,812.50
C) $73,677.21
D) $65,812.50
APR
Annual Percentage Rate, a measure that reflects the cost of borrowing on loans or credit cards or the yield from an investment, including interest and other fees.
Compounded Monthly
The process of adding interest to the principal sum of a loan or deposit, or in other words, interest on interest, calculated on a monthly basis.
Retirement Account
A financial account that is specifically designed to save funds for retirement, offering tax benefits for money invested and saved.
- Calculate the value of investments over time, considering compounding interest and contributions.
Verified Answer
SM
Shawn McCaffreyJul 27, 2024
Final Answer :
A
Explanation :
We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the initial deposit (or principal), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time (in years).
In this case, P = 750 (since that's how much Don deposits each month), r = 0.0325 (since the APR is 3.25%), n = 12 (since the interest is compounded monthly), and t = 15 (since that's how many years Don will be saving).
First, we need to calculate the total number of deposits that Don will make over the 15 years:
15 years x 12 months/year = 180 months
So Don will make 180 deposits of $750 each.
Now we can plug in the numbers and solve for A:
A = 750(1 + 0.0325/12)^(12*15)
A ≈ $173,677.27
Therefore, the best choice is A, and Don will have approximately $173,677.27 in his retirement account when he retires.
A = P(1 + r/n)^(nt)
where A is the final amount, P is the initial deposit (or principal), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time (in years).
In this case, P = 750 (since that's how much Don deposits each month), r = 0.0325 (since the APR is 3.25%), n = 12 (since the interest is compounded monthly), and t = 15 (since that's how many years Don will be saving).
First, we need to calculate the total number of deposits that Don will make over the 15 years:
15 years x 12 months/year = 180 months
So Don will make 180 deposits of $750 each.
Now we can plug in the numbers and solve for A:
A = 750(1 + 0.0325/12)^(12*15)
A ≈ $173,677.27
Therefore, the best choice is A, and Don will have approximately $173,677.27 in his retirement account when he retires.
Learning Objectives
- Calculate the value of investments over time, considering compounding interest and contributions.