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. $\$ 5500 ; 10 \%$ compounded monthly; 24 monthly 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.
$\$ 5500 ; 10 \%$ compounded monthly; 24 monthly payments

Key Concepts

Loan Amortization

Loan amortization refers to the process of paying off a debt over time through scheduled, equal payments. Each payment goes towards both the interest expense and reducing the principal balance. Understanding amortization is essential for analyzing how loans are repaid over a fixed period, determining the distribution of interest and principal, and planning future financial commitments.

Present Value of an Annuity

The present value of an annuity is a key financial concept that allows one to determine the current value of a series of future payments, given a specific interest rate. It is fundamental for computing the periodic payments required to fully amortize a loan over a specified term, ensuring that the sum of the discounted payments equals the initial loan amount.

Interest Rate Conversion

Interest rate conversion is the process of translating an annual interest rate to a periodic rate that corresponds to the payment frequency, such as monthly or quarterly. This conversion is crucial in loan amortization calculations because the payment formulas require the rate per compounding period, which ensures accurate computation of both interest and principal repayment portions.

Payment Computation Formula

The payment computation formula, often derived from the annuity formula, is used to calculate the fixed periodic payment necessary to amortize a loan. This formula takes into account the principal, the periodic interest rate, and the total number of payments, providing a methodical way to determine the consistent cash flow required to retire the debt over its term.

Amortization Schedule

An amortization schedule is a detailed table that outlines each loan payment over the repayment period. It breaks down each payment into interest and principal components, shows the reduction in the outstanding principal over time, and ultimately helps in understanding the progression of the loan repayment, including the total amount paid and the cumulative interest expense.

Transcript

00:01 Okay, so for part a, we're looking for our periodic payment value.

00:04 We're given the present value of the loan as $5 ,500.

00:14 We're given that the interest rate is 10%, but it's compounded monthly.

00:19 So it's going to be the i value.

00:21 We're going to use a 0 .1, 0 .10, or just 0 .1, divided by 12.

00:31 And our number of periods is going to be for 24 months.

00:44 Okay, so we can calculate this by using a formula.

00:49 So our r value is equal to our present value, divided by 1 minus 1 plus our interest rate, so 1 plus 0 .1 over 12 to the negative 24th power, all divided by 0 .1 over 12.

01:17 Just be careful with all your units in the calculator.

01:22 Okay, i'm going to put that in the calculator now.

01:27 So we have 5500.

01:34 Okay, so we're going to have to do in parentheses 1 minus 1 plus.

01:39 I'm just going to keep all this in the calculator just so it keeps all of our rounding errors to a minimum.

01:45 1 plus 0 .1 over 12 to the negative 24th power, all divided by 0 .1 over 12.

01:56 So our monthly payment is going to have to be $253 .80.

02:09 Okay, so there's part a.

02:15 Okay, so part b, part a again, part b, we have $253 .80.

02:25 And we're going to multiply that about 24 to see how many total payments we've made.

02:37 The grand total we've paid out $6 ,091 and $20.

02:48 Okay, and then our present value of the loan was 5 ,500, which means that our interest, according to the formula, is going to be $591 .20.

03:16 Okay, so part c wants me to make an amortization table...

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