Jeremy takes out a 30-year mortgage of 220000 dollars at an annual interest rate of 7 percent compounded monthly, with the first payment due in one month. How much does he owe on the loan immediately after the 87th payment?
I have tried 204311.1024, but not successful
first we have to find the payment.
let it be p
i = .07/12 = .005833.. ----> I stored in my calculator for increased accuracy
PV = 220,000
n = 360
p( 1 - 1.0058333...^-360)/.0058333... = 220000
I got p = $1463.67
Value of debt if no payments had been made after 87 periods
= 220000(1.0058333...)^87 = 364910.84
value of 87 payments at that time
= 1463.67( 1.0058333..^87 - 1)/.0058333..
= 165273.50
outstanding balance = 364,910.84 - 165,273.50
= 199,637.34
Since you did not show any of your steps, I have no way of knowing where you went wrong.
To calculate the amount owed immediately after the 87th payment on a mortgage, we need to use the formula for calculating the remaining balance on a loan with monthly compounding.
The formula to calculate the remaining balance on a mortgage is:
B = P * (1 + r)^n - (A / r) * [(1 + r)^n - 1]
Where:
B = Remaining balance on the mortgage
P = Principal amount (loan amount)
r = Monthly interest rate (annual interest rate divided by 12 and converted to decimal form)
n = Total number of monthly payments
A = Monthly payment amount
In this case, we can plug in the given values:
P = $220,000
r = 7% / 12 / 100 = 0.00583 (monthly interest rate)
n = 30 * 12 = 360 (total number of monthly payments)
A = Monthly payment amount (which we need to calculate)
To find the monthly payment amount (A), we can use the formula:
A = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Plugging in the values:
A = $220,000 * (0.00583 * (1 + 0.00583)^360) / ((1 + 0.00583)^360 - 1)
A ≈ $1,465.79 (rounded to the nearest cent)
Now, we can use this monthly payment amount to calculate the remaining balance after the 87th payment (B):
B = $220,000 * (1 + 0.00583)^87 - ($1,465.79 / 0.00583) * [(1 + 0.00583)^87 - 1]
B ≈ $162,294.10 (rounded to the nearest cent)
Therefore, Jeremy owes approximately $162,294.10 on the loan immediately after the 87th payment.