3. You decide to borrow $200,000 to build a new house. The bank charges an interest rate of 6% compounded monthly. If you pay the loan back over 30 years, what will your monthly payment be [rounded to the nearest dollar]?
To calculate your monthly payment for a loan, you can use the formula for calculating the monthly payment on an amortizing loan. The formula is:
M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = Monthly payment
P = Loan amount
r = Monthly interest rate
n = Total number of payments
In this case, you have a loan amount of $200,000, an interest rate of 6% compounded monthly, and a loan term of 30 years (which is equivalent to 360 monthly payments).
First, let's calculate the monthly interest rate:
r = (6% / 100) / 12 = 0.005
Next, substitute the values into the formula and solve for M:
M = 200,000 * (0.005 * (1 + 0.005)^360) / ((1 + 0.005)^360 - 1)
Using a calculator or a spreadsheet, you can compute the value for M, which will be your monthly payment. Rounding to the nearest dollar:
M ≈ $1,199
Therefore, your monthly payment for the loan will be approximately $1,199.
To calculate your monthly payment, you can use the formula for the monthly payment on a loan:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]
Where:
M = Monthly payment
P = Principal loan amount
i = Monthly interest rate
n = Total number of monthly payments
In this case:
P = $200,000
i = 6% / 12 = 0.005 (monthly interest rate)
n = 30 years * 12 months = 360 (total number of monthly payments)
Now, let's substitute these values into the formula and calculate the monthly payment.
M = 200000 [ 0.005(1 + 0.005)^360 ] / [ (1 + 0.005)^360 - 1 ]
Calculating this equation will give us the monthly payment.