To help open a jewelry store, Chang borrowed money from his credit union. He took out a personal, amortized loan for $45,000, at an interest rate of 6.45%, with monthly payments for a term of 8 years.
For each part, do not round any intermediate computations and round your final answers to the nearest cent.
Find Changs monthly payment?
If Chang pays the monthly payment each month for the full term, find his total amount to repay the loan?
If Chang pays the monthly payment each month for the full term, find the total amount of interest he will pay?
i = .0645/12 = .....
n = 8(12) = 96
paym = p
p( 1 - (1+i)^-96 )/i = 45000
- you should know that formula as the PV , present value, formula
Once you have the payment p , use your Amount formula to find the amount of 96 payments of p
To find Chang's monthly payment, we can use the formula for calculating the monthly payment on an amortized 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 (annual interest rate divided by 12)
n = Total number of payments (number of years multiplied by 12)
Let's calculate Chang's monthly payment step by step:
P = $45,000
r = 6.45% / 100 / 12 = 0.005375 (monthly interest rate)
n = 8 * 12 = 96 (total number of payments)
M = $45,000 * 0.005375 * (1 + 0.005375)^96 / ((1 + 0.005375)^96 - 1)
Calculating this expression will give us Chang's monthly payment.
Now, let's calculate Chang's total amount to repay the loan. This is simply the monthly payment multiplied by the total number of payments:
Total amount to repay = Monthly payment * Total number of payments
Finally, to find the total amount of interest Chang will pay, we can subtract the initial loan amount from the total amount to repay the loan.
Total interest paid = Total amount to repay - Loan amount
Let's calculate these values step by step.