Find (a) the payment necessary to amortize each loan; (b)...

Find (a) the payment necessary to amortize each loan; (b) the total payments and the total amount of interest paid based on the calculated monthly payments, and (c) the total payments and total amount of interest paid based upon an amortization table. $\$ 90,000 ; 6 \%$ compounded annually; 12 annual payments

Find (a) the payment necessary to amortize each loan; (b) the total payments and the total amount of interest paid based on the calculated monthly payments, and (c) the total payments and total amount of interest paid based upon an amortization table.
$\$ 90,000 ; 6 \%$ compounded annually; 12 annual payments

Key Concepts

Loan Amortization

Loan amortization is the process of paying off a debt over time with regular, scheduled payments that cover both principal and interest. Over the life of the loan, each payment reduces the outstanding balance until it reaches zero. This concept is fundamental in finance for structuring and understanding how loans are repaid, ensuring that borrowers know how much they'll need to pay periodically to retire the debt by the end of the term.

Amortization Schedule

An amortization schedule, often presented as a table, details each loan payment's breakdown over time, showing how much of each payment goes toward interest and how much toward principal. This schedule helps borrowers and lenders track the gradual reduction of the loan balance and understand the evolving interest costs throughout the repayment period. It is essential for accurate financial planning and recording total interest paid over the duration of the loan.

Payment Calculation Formula

The payment calculation formula for an amortized loan determines the fixed periodic payment necessary to fully repay the loan by the end of its term. This formula takes into account the loan amount, the periodic interest rate, and the total number of payments. It is widely used in both academic and practical settings to structure payment schedules for mortgages, car loans, and other types of installment loans.

Total Interest Calculation

Total interest calculation involves determining the cumulative amount of interest paid over the term of the loan. This is typically found by summing all interest portions of the individual payments or subtracting the original principal from the total payments made. Understanding the total interest helps borrowers see the cost of financing beyond just repaying the principal, highlighting the overall cost of the loan.

Transcript

00:01 Okay, so this problem, we're calculating our ordinary annuity payments in order to add up to our present value, which is the value of the loan taken out.

00:13 So the value of the loan in this particular one is $90 ,000.

00:19 The interest rate is 6 % compounded annually, so it's just going to be 0 .06.

00:28 And so our number of payments is going to be equal to 12.

00:33 Okay, to calculate our r value, we're just going to do our 90 ,000 divided by 1 minus 1 plus our interest rate, 1 .06 to negative 12, all over 0 .06.

00:57 Okay, so my r value, our payment, let's go plug that in.

01:05 So we have 90 ,000, 12 easy payments at 6%.

01:18 Plugging it all into the calculator, each payment is going to have to be 10 ,734 and 93 cents.

01:35 Okay, that was part a.

01:40 Okay, so part b just wants me to use that to calculate how much is being paid.

01:46 So we have 10 ,734 and 93 cents.

01:54 And multiply that by 12 because we have 12 payments.

01:57 So we're going to end up paying $128 ,819.

02:18 And since the original loan was for $90 ,000, the amount that we're paying in interest according to this calculation is going to be $38 ,819 .16.

02:41 Okay, so part c, it wants us to create an amortization schedule.

02:45 So we're going to have x.

02:48 We're going to have the amount paid each period, the interest on each previous principle, the portion paid to the principal, and the principal...

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