Suppose you borrow $12,000, which you must pay back in 30 equal monthly payments, each of which includes a .8% interest charge on the unpaid balance.
a) How much will you need to pay each month?
b) How much money did the bank make on this deal?
I will assume the .8% is the monthly rate
let the payment be P
12000 = P(1 - 1.008^-30)/.008
a) solve for P , I got 451.51
b) what is 451.51(30) compared to 12000 ?
To calculate the monthly payment and the total interest charged, you can use the formula for calculating the monthly payment on a loan, known as the amortization formula:
M = P * r * (1 + r)^n / ((1 + r)^n - 1)
Where:
M = the monthly payment
P = the principal amount borrowed
r = the monthly interest rate
n = the total number of monthly payments
To begin, let's calculate the monthly payment (M):
a) Monthly Payment:
In this case, the principal amount borrowed (P) is $12,000, the interest rate (r) is 0.8% (0.008 as a decimal), and the number of monthly payments (n) is 30.
Plugging these values into the formula:
M = 12000 * 0.008 * (1 + 0.008)^30 / ((1 + 0.008)^30 - 1)
Calculating this expression will give you the amount you need to pay each month.
b) Total Interest Charged:
To determine how much money the bank made on this deal, you need to calculate the total interest charged. This can be calculated by subtracting the principal amount borrowed (P) from the total amount paid over the 30 monthly payments.
Total Amount Paid = Monthly Payment (M) * Number of Payments (n)
Total Interest Charged = Total Amount Paid - Principal Amount Borrowed (P)
By using the values we have already calculated, you can find the total interest charged.
Please note that this calculation assumes fixed monthly payments and no additional fees or charges. Also, keep in mind that this formula is a simplified calculation and may not take into account certain variations in loan terms or compounding periods that could affect the final amount.