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. $\$ 7400 ; 6.2 \%$ compounded semiannually; 18 semiannual 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.
$\$ 7400 ; 6.2 \%$ compounded semiannually; 18 semiannual payments

Key Concepts

Interest Rate Conversion

Interest rate conversion is the process of translating a nominal or quoted interest rate into an effective rate that matches the compounding and payment frequency. This is important when the compounding period does not naturally align with the payment period, as it ensures the correct amount of interest is applied during each payment period.

Amortization Schedule

An amortization schedule is a detailed table that breaks down each loan payment into the portions that go toward interest and principal reduction. This schedule illustrates how the balance of the loan decreases over time, enables the calculation of total payments and interest paid, and is essential for understanding the cost structure of the loan over its term.

Annuity Formula

The annuity formula is used to calculate fixed periodic payments needed to fully repay a loan or investment with interest over a set duration. This formula takes into account the interest rate per period, the number of payments, and the present value of the loan, thereby ensuring that the debt is fully amortized over the payment timeline.

Loan Amortization

Loan amortization is the process of paying off a debt over a period through regular, fixed payments. These payments cover both principal and interest so that, over time, the loan is completely repaid. Understanding amortization is crucial for determining the structure and amount of each payment as well as the overall cost of financing.

Transcript

00:01 Periodic payments will be given that the present value of the loan is $7 ,400.

00:12 We're given the interest rate of 6 .2%, but because it's compounded semi -annually, we're going to divide that by 2 to get 0 .031 as our i value.

00:24 And the number of periods, i believe it just gives it to us, and 8 is 18.

00:30 So sorry.

00:33 Okay, so to calculate our r value, we're just going to use our formula.

00:37 So we have r is equal to our p value, 7400 divided by.

00:45 We have one minus one plus our i value, so 1 .031 to the negative 18th power divided by our i value, which is 0 .031.

01:00 Now this is a calculation needed to be done in a calculator.

01:04 So i'm going to go drop it in.

01:08 So we have 7 ,400, 1 .031, and into the negative 18th power.

01:26 And so that number comes up to be, our periodic payment needs to be $542 .60.

01:40 Okay.

01:43 So for part b, it asks us to calculate how much we will be paying.

01:50 So that number was 542, 60.

01:56 So to figure out how much we'll be paying, we're just going to multiply that by 18 payments.

02:13 Okay, so we're going to be paying out $9 ,76 .86.

02:18 And 80 cents, which if our interest payment is 74, i mean, if our total, if the present value was 7 ,400, our contributions were 9 ,700.

02:32 That means the interest that we paid on this loan was $2 ,366 .80.

02:45 Okay.

02:47 For the next step, they want us to calculate the same values based on an amortization table.

02:57 So i've done these for the last few problems.

03:01 But the mortization table is going to have several columns.

03:04 So the payment number, the payment amount, the interest based on the previous principle, we have a lowercase p for the portion that's paid to principal, and a capital p...

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