If a loan was repaid by monthly payments of $9230.00 in 7.5 years at 6.15% compounded annually, how much interest was paid?
Well, well, well, looks like we have ourselves a loan question! Don't worry, I've got my giant calculator and a cup of coffee ready to crunch some numbers. Let's get to it!
To find out how much interest was paid, we need to calculate the total amount repaid and then subtract the original loan amount. So, first off, let's figure out how much was repaid over the 7.5 years.
We know the monthly payments were $9230.00, so let's multiply that by 12 to get the annual payment: $9230.00 * 12 = $110,760.00.
Now that we have the annual payment, let's find the total amount repaid over the duration of the loan. 7.5 years * $110,760.00 = $830,700.00.
But wait, there's more! Now we need to find the original loan amount, which we can do using the compound interest formula. The formula is like a secret handshake, but instead of a handshake, you get a loan amount. It's magical!
The formula for compound interest is: P = A / (1 + r/n)^(nt)
P is the original loan amount, A is the total amount repaid, r is the annual interest rate (in decimal form), n is the number of times interest is compounded per year, and t is the number of years.
So, we plug in our numbers and solve for P:
P = $830,700.00 / (1 + 0.0615/1)^(1 * 7.5)
P = $830,700.00 / 1.512
After doing some calculations, we find that P ≈ $549,397.71, which is the original loan amount.
Finally, let's calculate the interest paid by subtracting the original loan amount from the total amount repaid:
Interest = Total amount repaid - Original loan amount
Interest = $830,700.00 - $549,397.71
Interest ≈ $281,302.29.
So, my friend, approximately $281,302.29 of interest was paid on this loan. That's a lot of money, but hey, at least you got a good workout for your math muscles!
To find the amount of interest paid on a loan, we need to calculate the total amount repaid and deduct the principal amount borrowed.
Step 1: Convert the loan term to months.
Since the loan term is given in years, we can multiply it by 12 to convert it to months.
Loan term in months = 7.5 years × 12 months/year = 90 months.
Step 2: Calculate the total amount repaid.
The monthly payment is $9230. To find the total amount repaid, we multiply the monthly payment by the loan term in months.
Total amount repaid = Monthly payment × Loan term in months
Total amount repaid = $9230 × 90
Total amount repaid = $830,700
Step 3: Find the principal amount borrowed.
The principal amount borrowed is the initial loan amount.
To calculate the principal amount, we can use the formula for the present value of an annuity:
Present Value = (Annual Payment / Interest Rate) * (1 - (1 + Interest Rate)^(-Number of Periods))
Where:
Annual Payment = $9230 (monthly payment × 12)
Interest Rate = 6.15% = 0.0615
Number of Periods = 90 months (loan term in months)
Present Value = ($9230 / 0.0615) * (1 - (1 + 0.0615)^(-90))
Present Value ≈ $706,093.44
Therefore, the principal amount borrowed is approximately $706,093.44.
Step 4: Calculate the interest paid.
Interest paid = Total amount repaid - Principal amount borrowed
Interest paid = $830,700 - $706,093.44
Interest paid ≈ $124,606.56
Therefore, approximately $124,606.56 was paid in interest.
To calculate the interest paid on a loan, we need to have two key pieces of information: the monthly payment amount and the loan term. In this case, we have both.
First, let's convert the loan term from years to months. We multiply the number of years by 12 to get the total number of months: 7.5 years * 12 months/year = 90 months.
Next, we need to determine the total payment made over the loan term. Since the monthly payment amount is $9230.00, we multiply it by the number of months: $9230.00/month * 90 months = $830,700.00.
Now that we know the total payment made, we can calculate the interest paid on the loan. To do this, we subtract the original loan amount from the total payment. However, we don't have the original loan amount given in the question. So, we need to find it using the loan term, interest rate, and monthly payments.
To find the original loan amount, we need to use the formula for the present value of an ordinary annuity:
PV = PMT * [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present Value (original loan amount)
PMT = Monthly payment
r = Interest rate per period
n = Number of periods
In this case, PMT = $9230.00, r = 6.15% compounded annually (0.0615), and n = 90 months.
Now we can substitute these values into the formula and solve for PV:
PV = $9230.00 * [(1 - (1 + 0.0615)^(-90)) / 0.0615]
Calculating this gives us an original loan amount of $626,633.40 (rounded to the nearest cent).
Finally, we can calculate the interest paid by subtracting the original loan amount from the total payment made:
Interest paid = Total payment - Original loan amount
Interest paid = $830,700.00 - $626,633.40 = $204,066.60
Therefore, the amount of interest paid on the loan is $204,066.60.
P = Po(1+r)^n.
T = 7.5yr. * 12mo./yr. = 90 mo.
P = 9230/mo. * 90mo. = $830,700.
r = 0.0615.
n = 1comp./yr. * 7.5yrs. = 7.5 compounding periods.
Po = ?.
I = P-Po.