Determine the accrued interest and the final amount of a $10,000 investment with a 4.75% simple interest rate over a period of 13 years. Round the answers to two decimal places as needed.(1 point)
The accrued interest is $
and the final amount of the investment is $
.
The accrued interest is $4,750.00 and the final amount of the investment is $14,750.00.
wrong
Apologies for the error. To calculate the accrued interest, you can use the formula:
Accrued Interest = Principal * Interest Rate * Time.
In this case, the principal is $10,000, the interest rate is 4.75%, and the time is 13 years.
Accrued Interest = $10,000 * 0.0475 * 13 = $6,175
The final amount of the investment can be calculated by adding the accrued interest to the principal:
Final Amount = Principal + Accrued Interest
Final Amount = $10,000 + $6,175 = $16,175
So, the accrued interest is $6,175 and the final amount of the investment is $16,175.
Chris invests $15,000 in a retirement account with an annual interest rate of 3.4%. Find the final amount of the investment after 27 years if interest is compounded quarterly.
Round the answer to the nearest cent.(1 point)
The final amount of the investment after 27 years is $
.
To find the final amount of the investment, we can use the compound interest formula:
Final Amount = Principal * (1 + interest rate / number of compounding periods)^(number of compounding periods * time)
In this case, the principal is $15,000, the interest rate is 3.4% (converted to 0.034), and the time is 27 years. Since the interest is compounded quarterly, the number of compounding periods would be 4 (quarterly compounding).
Final Amount = $15,000 * (1 + 0.034/4)^(4 * 27)
Calculating this formula, the final amount is approximately $40,670.98.
Therefore, the final amount of the investment after 27 years, compounded quarterly, is $40,670.98.
When Martin was born, his father set up a $5,000 college fund for him with an annual compound interest rate of 7.3%. What is the final amount of this college fund, and how much interest is gained if this fund is invested for 18 years if interest is compounded monthly? Round the answers to two decimal places as needed.(1 point)
The final amount of the college fund is $
, and the amount of interest gained is $
.
To find the final amount of the college fund, we will use the compound interest formula:
Final Amount = Principal * (1 + (Interest Rate / Number of Periods))^Number of Periods * Time
In this case, the principal is $5,000, the interest rate is 7.3% (converted to 0.073), and the time is 18 years.
Since the interest is compounded monthly, the number of periods would be 12 (monthly compounding).
Final Amount = $5,000 * (1 + (0.073 / 12))^(12 * 18)
Calculating this formula, the final amount of the college fund is approximately $14,404.02.
To calculate the amount of interest gained, we subtract the principal from the final amount:
Interest Gained = Final Amount - Principal
Interest Gained = $14,404.02 - $5,000 = $9,404.02
Therefore, the final amount of the college fund is $14,404.02 and the amount of interest gained is $9,404.02.
Financial Literacy Unit Test
4 of 134 of 13 Items
Question
Angel wants to invest $7,000 for 3 years. He has two investing options.
Option 1: Investing with a 15% simple interest rate.
Option 2: Investing with a 12% compound interest rate, with interest being compounded quarterly.
Find the difference in interest earnings to help Angel determine which investing option will give more financial returns.
(1 point)
The difference in interest earnings is $
, and option
is the better investing option
To find the difference in interest earnings, we need to calculate the interest earned for each option and then find the difference between the two.
For Option 1, with a simple interest rate of 15%, we can calculate the interest earned using the formula:
Interest = Principal * Interest Rate * Time
Interest = $7,000 * 0.15 * 3 = $3,150
For Option 2, with a compound interest rate of 12%, compounded quarterly, we can use the formula:
Final Amount = Principal * (1 + (Interest Rate / Number of periods))^(Number of periods * Time)
Final Amount = $7,000 * (1 + (0.12 / 4))^(4 * 3) = $7,829.02
Interest earned in Option 2 = Final Amount - Principal = $7,829.02 - $7,000 = $829.02
The difference in interest earnings = Interest earned in Option 2 - Interest earned in Option 1 = $829.02 - $3,150 = -$2,320.98
Given that the difference in interest earnings is -$2,320.98, it means that Option 1 (15% simple interest rate) has a higher interest earning compared to Option 2 (12% compound interest rate).