You borrowed $10,400 for 4 years at 12.7% and the interest is compounded semiannually. What is the total you will pay back?
First, we need to calculate the semiannual interest rate. We divide the annual rate (12.7%) by 2 because interest is compounded twice a year:
Semiannual interest rate = 12.7% / 2 = 6.35%
Next, we need to calculate the number of compounding periods. Since the loan is for 4 years and interest is compounded twice a year, there are 8 compounding periods:
Number of compounding periods = 4 years x 2 = 8 periods
Now we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the total amount paid back
P = the principal (initial amount borrowed) = $10,400
r = the semiannual interest rate = 6.35%
n = the number of compounding periods per year = 2
t = the total number of years = 4
Plug in the values and solve:
A = $10,400(1 + 0.0635/2)^(2x4)
A = $10,400(1.03175)^8
A = $15,710.05
Therefore, the total amount paid back (including principal and interest) is $15,710.05.
1. A bank is offering 2.5% simple interest on a savings account. If you deposit $5000, how much interest will you earn in one year?
To calculate the interest earned on a savings account with simple interest, we use the formula:
Interest = Principal x Rate x Time
where:
- Principal = $5000 (initial amount deposited)
- Rate = 2.5% (per year)
- Time = 1 year
Plug in the values and solve:
Interest = $5000 x 0.025 x 1
Interest = $125
Therefore, you will earn $125 in interest on your savings account in one year at a rate of 2.5% simple interest.
2) If Michael invests $2000 in the bank at a rate of 5.5% for 6 years how much interest will he make?
To calculate the interest earned with compound interest, we can use the formula:
A = P(1 + r/n)^(nt)
where:
- A is the total amount at the end of the 6-year period
- P is the initial principal amount of $2000
- r is the annual interest rate of 5.5%
- n is the number of times the interest is compounded per year
- t is the time period of 6 years
Since the problem does not specify how frequently the interest is compounded, we will assume that it is compounded annually (n = 1).
Plugging in the values, we get:
A = $2000(1 + 0.055/1)^(1x6)
A = $2000(1.055)^6
A = $2894.21 (rounded to the nearest cent)
To find the interest earned, we subtract the initial principal amount from the final amount:
Interest = $2894.21 - $2000
Interest = $894.21
Therefore, Michael will earn $894.21 in interest over 6 years at a rate of 5.5% compounded annually.
2. To buy a car, Jessica borrowed $15,000 for 3 years at an annual simple interest rate of 9%. 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?
To calculate the interest paid on a loan with simple interest, we can use the formula:
Interest = Principal x Rate x Time
where:
- Principal = $15,000 (initial amount borrowed)
- Rate = 9% (per year)
- Time = 3 years
Plug in the values and solve for the interest:
Interest = $15,000 x 0.09 x 3
Interest = $4,050
Therefore, Jessica will pay $4,050 in interest if she pays off the entire loan at the end of the third year.
To find the total amount she will have to repay, we add the initial principal amount to the interest:
Total amount = Principal + Interest
Total amount = $15,000 + $4,050
Total amount = $19,050
Therefore, Jessica will have to repay a total of $19,050 over 3 years at an annual rate of 9% simple interest.
1.) You invested $52,400 at 6% compounded annually for 5 years. What is your total return on this investment?
To calculate the total return on an investment with compound interest, we can use the formula:
Total return = Final amount - Initial amount
where:
- Initial amount = $52,400 (the principal amount invested)
- Final amount = the amount after 5 years with compound interest.
To calculate the final amount with compound interest, we can use the formula:
A = P(1 + r/n)^(nt)
where:
- A is the final amount
- P is the principal amount of $52,400
- r is the annual interest rate of 6%
- n is the number of times the interest is compounded per year, which is 1 for annual compounding
- t is the time period of 5 years.
Plugging in the values, we get:
A = $52,400(1 + 0.06/1)^(1x5)
A = $68,886.70 (rounded to the nearest cent)
Therefore, the final amount after 5 years with compound interest is $68,886.70.
Now we can calculate the total return:
Total return = Final amount - Initial amount
Total return = $68,886.70 - $52,400
Total return = $16,486.70
Therefore, the total return on the investment is $16,486.70 over a period of 5 years at an annual rate of 6% compounded annually.