Question

lisa borrows $10,000 from a local bank so she can return to school. she secures a fixed rate of 4.15 nd agrees to repay the loan over the next 15 years.

Answer 1

Lisa's monthly payment is approximately $74.72

Lisa borrows $10,000 at a fixed interest rate of 4.15% annually and agrees to repay the loan over 15 years. Assuming she's making monthly payments, the loan will be an amortized loan with fixed monthly payments.

To calculate her monthly payment, we can use the formula for the monthly payment on an amortized loan, which is:

`\[ P = (L * i)/(1 - (1 + i)^(-n)) \]`

where:

- P is the monthly payment

- L is the loan amount ($10,000)

- i is the monthly interest rate (annual rate divided by 12 months)

- n is the total number of payments (15 years times 12 months per year)

First, we'll calculate the monthly interest rate:

`\[ i = (4.15\%)/(12) = (0.0415)/(12) \approx 0.00345833 \]`

Next, we'll calculate the total number of payments:

`\[ n = 15 * 12 = 180 \]`

Now we can plug these numbers into the formula:

`\[ P = (10000 * 0.00345833)/(1 - (1 + 0.00345833)^(-180)) \]`

Let's calculate this to find Lisa's monthly payment.

Lisa's monthly payment, calculated to the nearest cent, will be approximately $74.72. This is the fixed amount she will need to pay each month for the next 15 years to repay the $10,000 loan with a fixed annual interest rate of 4.15%.

lisa borrows $10,000 from a local bank so she can return to school. she secures a fixed rate of 4.15 nd agrees to repay the loan over the next 15 years.what is lisa's monthly pay?

Answer 2

Lisa's fixed-rate loan of $10,000 at 4.15% over 15 years results in a monthly payment of approximately $73.76.

Step-by-step explanation:

Lisa's loan amount is $10,000 with a fixed interest rate of 4.15% over 15 years. To calculate the monthly payment, we can use the formula for a fixed-rate mortgage payment, known as the loan amortization formula:

`\[PMT = (P \cdot r \cdot (1 + r)^n)/((1 + r)^n - 1)\]`

Where:

- (PMT) is the monthly payment,

- (P) is the principal amount (loan amount),

- (r) is the monthly interest rate (annual rate divided by 12 and converted to a decimal), and

- (n) is the total number of payments (loan term in years multiplied by 12).

In Lisa's case:

- (P = $10,000),

-
`\(r = (4.15\%)/(12) = 0.003458\)`,

-
`\(n = 15 * 12 = 180\).`

Substituting these values into the formula, we get:

`\[PMT = (\$10,000 \cdot 0.003458 \cdot (1 + 0.003458)^(180))/((1 + 0.003458)^(180) - 1)\]`

After evaluating this expression, the monthly payment comes out to be approximately $73.76.

Therefore, Lisa's monthly payment for the loan is approximately $73.76. This calculation assumes a constant monthly interest rate and does not account for potential changes due to factors such as fees or prepayments. It provides a baseline estimate for her regular repayment schedule over the 15-year period.