50,000 is the amount of a loan needed to purchase a restaurant location. After researching to find the best interest rate, you find that banks for small business offer the best interest rate at 9% compounded monthly for 7 years. After making a monthly payment of $804.45 monthly for 6 years what is your remaining balance
What is your remaining balance.
To calculate the remaining balance on the loan after making monthly payments for 6 years, we can use the formula for calculating the future value of a loan with monthly compounding interest.
The formula for the future value (FV) of a loan with monthly compounding interest is:
FV = PV(1 + r/n)^(nt) - PMT((1+r/n)^(nt) - 1) / (r/n)
Where:
PV = Loan amount (present value) = $50,000
r = Annual interest rate (as a decimal) = 9% or 0.09
n = Number of compounding periods per year = 12 (monthly payments)
t = Number of years = 7
PMT = Monthly payment = $804.45
First, we need to calculate the remaining time in years (t') after making monthly payments for 6 years. Since the loan term is 7 years, the remaining time can be calculated as:
t' = t - 6 = 7 - 6 = 1 year
Now, let's calculate the remaining balance (FV'):
FV' = PV(1 + r/n)^(nt') - PMT((1+r/n)^(nt') - 1) / (r/n)
FV' = $50,000(1 + 0.09/12)^(12*1) - $804.45((1+0.09/12)^(12*1) - 1) / (0.09/12)
Now, we can plug the values into the equation and calculate the remaining balance:
FV' = $50,000(1 + 0.0075)^(12) - $804.45((1+0.0075)^(12) - 1) / 0.0075
Calculating this, we find that the remaining balance after 6 years of payments would be approximately $12,175.31.