Susan Borrowed $5000. The term of the loan is 12% compouned monthly for 3 years.

what is the monthly payments?
How much must she pay at the end of of 1 year to pay the balance off?
How much did she save in interest by paying the loan off in one year??

payment for the 3-year plan:

i = .12/12 = .01
n = 36
payment = x
x ( 1 - 1.01^-36 )/.01 = 5000
x (30.10750504) = 5000
x = 166.07

balance owing at the end of 1 year
= 5000(1.01)^12 - 166.07(1.01^12 - 1)/.01
= 3527.92

Can you take if from there ?

To calculate the monthly payments, we can use the formula for calculating the monthly payment amount of a loan:

Monthly Payment = (P * r * (1+r)^n) / ((1+r)^n - 1)

Where:
P = Principal amount borrowed = $5000
r = Monthly interest rate = Annual interest rate / 12 = 12% / 12 = 1%
n = Total number of monthly payments = 3 years * 12 months/year = 36 months

Substituting the values into the formula:

Monthly Payment = (5000 * 0.01 * (1+0.01)^36) / ((1+0.01)^36 - 1)

Calculating this, the monthly payment amount would be approximately $166.50.

To calculate how much Susan must pay at the end of 1 year to fully pay off the balance, we need to calculate the remaining balance after 1 year. Since the loan is compounded monthly, we can use the compound interest formula:

A = P * (1 + r)^n

Where:
A = Future value or balance after n months
P = Principal amount borrowed
r = Monthly interest rate
n = Total number of months

Substituting the values into the formula:

A = 5000 * (1 + 0.01)^12

Calculating this, the balance after 1 year would be approximately $5634.30.

Therefore, Susan would need to pay approximately $5634.30 to fully pay off the balance at the end of 1 year.

To calculate how much she saved in interest by paying off the loan in one year, we can subtract the interest paid over 1 year from the total interest paid over 3 years.

To calculate the total interest paid over 3 years, we can use the formula:

Total Interest Paid = Total Payment (36 months) - Principal Amount

Total Payment = Monthly Payment * Number of Payments (36 months)

Substituting the values into the formula:

Total Payment = 166.50 * 36 = $5994

Total Interest Paid = $5994 - $5000 = $994

To calculate the interest paid over 1 year, we need to find the balance after 1 year and subtract the original principal.

Interest Paid over 1 Year = Balance after 1 year - Principal Amount

Interest Paid over 1 Year = $5634.30 - $5000 = $634.30

Therefore, Susan saved approximately $994 - $634.30 = $359.70 in interest by paying off the loan in one year.

To calculate the monthly payments on a loan, we can use the formula for the future value of an ordinary annuity:

Future Value = P * [(1 + r)^n - 1] / r,

where P is the principal amount (loan amount), r is the monthly interest rate, and n is the number of months.

1. Monthly Payments:

Given:
Principal amount (P) = $5000
Annual interest rate = 12%
Compounding frequency = Monthly
Loan term = 3 years

First, we need to find the monthly interest rate by dividing the annual interest rate by 12:

Monthly interest rate (r) = Annual interest rate / 12 = 12% / 12 = 1%.

Next, we calculate the total number of months (n) by multiplying the loan term (3 years) by 12:

Total number of months (n) = Loan term * 12 = 3 * 12 = 36 months.

Now we can plug the values into the formula:

Future Value = $5000 * [(1 + 0.01)^36 - 1] / 0.01.

Using a calculator or spreadsheet, evaluate the formula to find the monthly payments.

2. Amount to be paid at the end of 1 year:

To determine how much Susan must pay at the end of 1 year to pay off the balance, we need to calculate the remaining loan balance after 1 year. This can be done using the formula for compound interest:

Future Value = P * (1 + r)^n,

where P is the principal amount (loan amount), r is the monthly interest rate, and n is the number of months.

Given:
Principal amount (P) = $5000
Monthly interest rate (r) = 1%
Number of months (n) = 12

Plug the values into the formula:

Future Value = $5000 * (1 + 0.01)^12.

Evaluate the formula using a calculator or spreadsheet to find the amount Susan must pay at the end of 1 year to pay off the balance.

3. Amount saved in interest by paying off the loan in one year:

To calculate the amount saved in interest by paying off the loan in one year, we need to find the difference between the interest paid over 3 years and the interest paid over 1 year.

First, calculate the total interest paid over 3 years using the formula for compound interest:

Total Interest = Future Value - Principal amount.

Given:
Principal amount (P) = $5000
Monthly interest rate (r) = 1%
Number of months (n) = 36

Calculate the future value using the formula mentioned earlier:

Future Value = $5000 * [(1 + 0.01)^36 - 1] / 0.01.

Evaluate the formula to find the total interest paid over 3 years.

Next, calculate the interest paid over 1 year using the same formula with modified values:

Principal amount (P) = Remaining loan balance at the end of 1 year
Monthly interest rate (r) = 1%
Number of months (n) = 12

Calculate the future value using the formula:

Future Value = Remaining loan balance at the end of 1 year * (1 + 0.01)^12.

Evaluate the formula to find the interest paid over 1 year.

Finally, subtract the interest paid over 1 year from the total interest paid over 3 years to find the amount saved in interest.