Loan Payments - If you take out an $8,000 car loan that calls for 48 monthly payments APR of 10 percent, what is your monthly payment? What is the effecgive annual interest rate on the loan?

the montly rate is 0.10/12=.0083333...

then 8000= payment[1-(1.0083333)^-48]/0.00833333

solving this I got payment = 202.90

let the annual rate be j

then (1+j)^1=1.00833333^12
1+j=1.1047131
j=0.1047..
or the effective rate is 10.47%

An AT&T bond has 10 years until maturity, a coupon rate of 8 percent, and sells for $1,100.

a. What is the current yield on the bond?
b. What is the yield to maturity?

To find the monthly payment, you can use the formula:

Payment = Loan Amount / [1 - (1 + Monthly Interest Rate)^(-Number of Months)]

In this case, the loan amount is $8,000 and the number of months is 48. The monthly interest rate can be calculated by dividing the APR by 12.

Monthly Interest Rate = APR / 12 = 10% / 12 = 0.00833333 (rounded)

Plugging in the values, we get:

Payment = 8000 / [1 - (1 + 0.00833333)^(-48)]

Using a calculator or spreadsheet, solving this equation gives a monthly payment of $202.90 (rounded to two decimal places).

To find the effective annual interest rate, we need to find the rate that, when compounded annually, yields the same result as the given monthly rate. We can use the formula:

(1 + Effective Annual Interest Rate)^12 = (1 + Monthly Interest Rate)^48

We know that the monthly interest rate is 0.00833333, so we can solve for the effective annual interest rate:

(1 + Effective Annual Interest Rate)^12 = (1 + 0.00833333)^48

Simplifying this equation, we find:

1 + Effective Annual Interest Rate = (1 + 0.00833333)^12

Taking the twelfth root of both sides, we have:

1 + Effective Annual Interest Rate = 1.1047131

Subtracting 1 from both sides gives:

Effective Annual Interest Rate = 1.1047131 - 1 = 0.1047131

This means the effective annual interest rate on the loan is 10.47% (rounded to two decimal places).

To calculate the monthly payment on a loan, you can use the formula:

Payment = Loan Amount [Interest Rate (1 + Interest Rate)^Number of Payments] / [(1 + Interest Rate)^Number of Payments - 1]

In this case, the loan amount is $8,000, the interest rate is 10% APR (Annual Percentage Rate), and the number of payments is 48 (monthly payments).

First, we need to calculate the monthly interest rate. Divide the annual interest rate by 12 to get the monthly rate: 10% / 12 = 0.0083333...

Now, substitute these values into the formula:

Payment = $8,000 [0.0083333... (1 + 0.0083333...)^48] / [(1 + 0.0083333...)^48 - 1]

Simplifying the equation, we get:

Payment = $8,000 [0.0083333... (1.0083333...)^48] / [(1.0083333...)^48 - 1]

Calculating this expression will give us the monthly payment:

Payment ≈ $202.90

So, the monthly payment on this loan would be approximately $202.90.

To find the effective annual interest rate on the loan, we need to calculate the annual interest rate that would have the same effect as the stated 10% APR over one year.

To do this, we can use the formula for compound interest:

(1 + Annual Interest Rate)^1 = (1 + Monthly Interest Rate)^12

where the monthly interest rate is 0.0083333...

Simplifying the equation, we get:

(1 + Annual Interest Rate) = (1.0083333...)^12

Solving for the annual interest rate:

Annual Interest Rate ≈ 0.1047...

So, the effective annual interest rate on this loan is approximately 10.47%.