To buy a laptop computer, Elaine borrowed $2,000 for 3 years at an annual simple interest rate of 5%. How much interest will she pay if she pays the entire loan off at the end of the third year? What is the total amount that she will repay?
The interest Elaine will pay is calculated as follows:
Interest = Principal x Rate x Time
Interest = $2,000 x 0.05 x 3
Interest = $300
Therefore, Elaine will pay $300 in interest if she pays the entire loan off at the end of the third year.
The total amount that Elaine will repay includes the original loan amount and the interest. Therefore:
Total amount = Principal + Interest
Total amount = $2,000 + $300
Total amount = $2,300
Therefore, Elaine will repay a total of $2,300 if she pays the entire loan off at the end of the third year.
Determine the amount of interest earned on a $100,000 investment if it is invested at 5.2% annual interest compounded quarterly for 12 years.
The formula for calculating compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the total amount (including principal and interest)
P = the principal amount
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
Using this formula, we can calculate the interest earned on a $100,000 investment at 5.2% annual interest compounded quarterly for 12 years:
A = 100000(1 + 0.052/4)^(4*12)
A = $181,136.28
Subtracting the principal amount from the total amount gives us the amount of interest earned:
Interest = $181,136.28 - $100,000
Interest = $81,136.28
Therefore, the amount of interest earned on a $100,000 investment at 5.2% annual interest compounded quarterly for 12 years is $81,136.28.
Ndiba invests a sum of money in a savings account with a fixed annual interest rate of 4.61% compounded 3 times per year. After 6 years, the balance reaches $5,485.85. What was the amount of the initial investment?
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (balance)
P = the principal (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
We know that the interest rate is 4.61% compounded 3 times per year, or 4.61/3 = 1.54% per compounding period. We also know that the balance after 6 years is $5,485.85. Plugging in these values and solving for the principal:
$5,485.85 = P(1 + 0.0154)^(3*6)
$5,485.85 = P(1.0154)^18
$5,485.85 = P(1.3122)
P = $4,178.60
Therefore, Ndiba's initial investment was $4,178.60.
Your investment of $18,100 at 13.6% compounded quarterly for 71/2 years will be worth how much?
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
First, we need to convert the given annual interest rate of 13.6% to a quarterly interest rate. We can do this by dividing 13.6% by 4 (since interest is compounded quarterly):
r = 13.6% / 4
r = 0.136 / 4
r = 0.034
Now we can plug in the values we know:
A = $18,100(1 + 0.034)^(4*7.5)
A = $18,100(1.034)^30
A = $18,100(2.899)
A = $52,578.60
Therefore, the investment of $18,100 at 13.6% compounded quarterly for 7.5 years will be worth $52,578.60.
Your 6 and 2/3 year investment of $1,450 at 5.4% compounded monthly brought you a grand total of?
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
First, we need to convert the given annual interest rate of 5.4% to a monthly interest rate. We can do this by dividing 5.4% by 12 (since interest is compounded monthly):
r = 5.4% / 12
r = 0.0045
Now we can plug in the values we know:
A = $1,450(1 + 0.0045)^(12*6.67)
A = $1,450(1.0045)^80
A = $1,450(1.4098)
A = $2,045.41
Therefore, the investment of $1,450 at 5.4% compounded monthly for 6 and 2/3 years will be worth $2,045.41.