# Algebra

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You find that a small business loan in the amount of 50,000 is the amount you need to purchase the restaurant location. After researching banks to find the best interest rate, you find that banks for small businesses offer the best interest rate of 9% interest that compounds monthly for 7 years.

What is the monthly payment for this loan?
Show the formula that you used and the values used for each variable to calculate the monthly payment.
What is the unpaid balance of the loan at the end of the 1st year?
Show the formula that you used and the values used for each variable to calculate the unpaid balance at the end of the 1st year.
What is the unpaid balance at the end of the 6th year? Show the formula that you used and the values used for each variable to calculate the unpaid balance at the end of the 6th year.

• Algebra -

i = .09/12 = .0075
n = 12(7) = 84
let the payment be P

50000 = P(1 - 1.0075^-84)/.0075
P = 804.45

balance after 1 year
= 50000(1.0075)^12 - 804.45(1.0075^12 - 1)/.0075
= 44628.62

do the same steps for the last part of your question.

• Algebra -

Could you please show me all the steps. I really need to understand this. there are 3 parts to be answered. I am so confused
Thank you so much..

• Algebra -

I used the formula
Amount of single lump sum of money
= Principal (1 + i)^n

the present value of an annuity
PV = P( 1 - (1+i)^-n)/i

and the amount of an annuity
amount = P( (1+i)^n - 1)/i

where P is the annuity payment, i is the interest rate of each period expressed as a decimal and n is the number of periods

I showed all the steps necessary, I am sure you can insert any intermediate arithmetic answers if you need them

• Algebra -

Balance owed at end of year 6
= 50000(1.0075)^72 - 804.45(1.0075^72 - 1)/.0075 = \$9,198.86

Total repayment+ \$67,574.13 based on \$50,000 at 9% for 7 years.

Is this correct? Thanks for your help

• Algebra -

balance after 6 years
= 50000(1.0075)^72-804.45(1.0075^72 - 6)/.0075= 9198.86

• Algebra -