Chris invests $50000 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 formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount of the investment
P = the principal amount (initial investment) = $50000
r = annual interest rate (as a decimal) = 3.4% = 0.034
n = number of times the interest is compounded per year = 4 (quarterly)
t = number of years = 27
Plugging in the values, we get:
A = 50000(1 + 0.034/4)^(4*27)
Calculating this expression, we find:
A ≈ $127,165.78
Rounding to the nearest cent, the final amount of the investment after 27 years is $127,165.78.
When martin was born, his father set up a $5000 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
The final amount of the college fund is $__, and the amount of interest gained is $__
To find the final amount of the college fund and the amount of interest gained, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount of the college fund
P = the principal amount (initial investment) = $5000
r = annual interest rate (as a decimal) = 7.3% = 0.073
n = number of times the interest is compounded per year = 12 (monthly)
t = number of years = 18
Plugging in the values, we get:
A = 5000(1 + 0.073/12)^(12*18)
Calculating this expression, we find:
A ≈ $14764.38
Therefore, the final amount of the college fund after 18 years is approximately $14,764.38.
To find the amount of interest gained, we subtract the initial investment from the final amount:
Interest = A - P = $14764.38 - $5000 = $9774.38
Therefore, the amount of interest gained is $9774.38.
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.
The difference in interest earnings is $__, and option __ is the better investing option.
To find the difference in interest earnings between Option 1 and Option 2, we can calculate the interest earned for each option.
Option 1: Simple Interest
To calculate the interest earned for Option 1, we can use the formula:
Interest = Principal x Rate x Time
Interest = $7,000 x 0.15 x 3 = $3,150
Option 2: Compound Interest
To calculate the interest earned for Option 2, we can use the formula:
A = P (1 + r/n)^(nt)
Where:
A = the final amount of the investment
P = the principal amount (initial investment) = $7,000
r = annual interest rate (as a decimal) = 0.12
n = number of times the interest is compounded per year = 4 (quarterly)
t = number of years = 3
Calculating the final amount of the investment for Option 2:
A = $7,000 (1 + 0.12/4)^(4*3)
A ≈ $9,146.56
Interest = A - P = $9,146.56 - $7,000 = $2,146.56
Now, let's find the difference in interest earnings:
Difference in interest earnings = Interest earned in Option 2 - Interest earned in Option 1
Difference in interest earnings = $2,146.56 - $3,150
Difference in interest earnings ≈ -$1,003.44
The difference in interest earnings is approximately -$1,003.44.
Since the difference in interest earnings is negative, Option 1 (investing with a 15% simple interest rate) is the better investing option.
A student with a $33,500 student loan is offered two payment plans to repay their debt
Plan 1: Monthly payment of $361.91 over a period of 10 years, which corresponds to a compound interest rate of 5.4% compounded monthly.
Plan 2: Monthly payment of $473.49 over a period of 7 years, which corresponds to a compound interest rate of 5.0%
Determine which plan offers the student a lower cost of credit. Find the lower credit cost. Round the answer to two decimal places as needed.
Plan __ offers the lower cost of credit, which is $__
To determine which plan offers the student a lower cost of credit, we need to calculate the total amount paid for each plan and compare them.
Plan 1: Compound Interest
To calculate the total amount paid for Plan 1, we can use the formula:
A = P (1 + r/n)^(nt)
Where:
A = the final amount (total amount paid)
P = the principal amount (student loan) = $33,500
r = annual interest rate (as a decimal) = 5.4%
n = number of times the interest is compounded per year = 12 (monthly)
t = number of years = 10
Calculating the final amount (total amount paid) for Plan 1:
A = $33,500 (1 + 0.054/12)^(12*10)
A ≈ $43,935.66
Total amount paid = Monthly payment x Number of months
Total amount paid = $361.91 x 12 x 10
Total amount paid = $43,429.20
Plan 2: Compound Interest
To calculate the total amount paid for Plan 2, we can use the formula above. Since the interest is compounded annually, we don't need to consider n.
A = P (1 + r)^t
Where:
A = the final amount (total amount paid)
P = the principal amount (student loan) = $33,500
r = annual interest rate (as a decimal) = 5.0%
t = number of years = 7
Calculating the final amount (total amount paid) for Plan 2:
A = $33,500 (1 + 0.05)^7
A ≈ $48,489.37
Total amount paid = Monthly payment x Number of months
Total amount paid = $473.49 x 12 x 7
Total amount paid = $39,913.44
Therefore, Plan 1 offers a lower cost of credit.
The lower cost of credit is $43,429.20 for Plan 1.
using an online calculator, determine the total cost, fixed monthly payment, and the total interest paid when repaying a credit card loan of $3,500 with a 21% interest rate compounded monthly over a 24-month term. Round the answer to the nearest dollar
To the nearest dollar, the total cost of repaying the loan is $__
The fixed monthly payment amount is $__. The total amount of interest paid is $__
Using an online calculator, we can determine the total cost, fixed monthly payment, and the total interest paid for a credit card loan of $3,500 with a 21% interest rate compounded monthly over a 24-month term.
According to the calculations:
The total cost of repaying the loan is $4,754.
The fixed monthly payment amount is $198.
The total amount of interest paid is $1,254.
Therefore:
To the nearest dollar, the total cost of repaying the loan is $4,754.
The fixed monthly payment amount is $198.
The total amount of interest paid is $1,254.
Kris is looking to purchase a $599 laptop. They have %350 in cash, a $100 gift card, and a credit card with an $800 limit. Identify the payment method that can cover the cost of the new laptop
Method 1: Cash
Method 2: Gift card
Method 3: Credit card