Consider a 5 year amortized loan with a fixed annual payment...

Consider a 5-year amortized loan with a fixed annual payment of $1,000, and an APR of 8%. At the start of the second year, the outstanding principal balance is $3,312. What is the amount of principal paid off during the second year?

Transcript

00:01 So you're about to borrow a loan amount of $10 ,000 from a bank at an interest rate r of 9 % which is 0 .09 and you're gonna be making payments in the amount of $2 ,570 .92 with the first payment occurring at the end of year one so then for each year show the payment and principal payment or the interest payment and the principal payment well, let's see t the payment the interest the principal repaid and the outstanding balance we start with at time zero the loan amount 10 ,000 our payment is gonna be the same every year so two seventy point ninety two two five seventy point ninety two two five seventy point ninety two two five seventy point ninety two but we don't make a payment in year zero so here we just have the balance at time zero and then two five seventy point ninety two well, the interest is gonna be the previous balance so b t minus one times r so that then is gonna be let's see here for the interest during period t that is gonna be 10 ,000 times 0 .09 so this is gonna be 900 and the principal repaid is gonna be two five seventy point ninety two minus a nine hundred which is sixteen seventy point ninety two and we subtract that then from the previous balance this is the payment minus the interest paid so, let's see how i subtract this from 10 ,000 and it gives me eight thousand three hundred twenty nine dollars and eight cents and i multiply that by my interest rate zero point zero nine to get the interest in my second payment.

02:49 So seven forty nine point sixty two and then subtract that from the two five seven zero point ninety two my payment amount and it gives me a principal repayment of eighteen hundred twenty one dollars and thirty cents in my second loan payment and that reduces then my previous balance so subtract that from eighty three twenty nine point zero eight and my new balance is six five zero seven point seven eight then i take that then multiply it by zero point zero nine to get my new interest payment five eight five point seven zero subtract that from two five seven zero point ninety two that gives me my principal nineteen -eighty -five point twenty two subtract that from the sixty five.

03:50 Oh seven point seventy eight to get my new balance four five two two point five six then multiplied it by the interest rate zero nine my new interest is going to be four oh seven point zero three subtract that from two five seven zero point ninety two it gives me my oops, i that okay...

Question

Consider a 5-year amortized loan with a fixed annual payment of $1,000, and an APR of 8%. At the start of the second year, the outstanding principal balance is $3,312. What is the amount of principal paid off during the second year?

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