Question

Your dream is finally coming true! You've saved and saved and are about to become a homeowner! After a conversation with your banker, you've agreed to a 20% down payment on your $182,188 home. To keep this problem and your calculations relatively brief, assume that the bank has offered you a mortgage loan for $145,750 that carries a 6% interest rate, semiannual payments of $26,905, and a 3-year term. Remember, the process is the same when you are preparing for either 6 semiannual payments of nearly $27,000 or 360 monthly payments of $873.85 for a 30-year conventional mortgage. Complete the following loan amortization table by entering the correct answers. Notes: 1. As all values are denominated in U.S. dollars, you do not have to enter any dollar signs 2. Round all interest payments down to the nearest whole dollar. 3. Rounding creates a situation in which the numbers in the loan's final payment are often unequal. Notice in this problem, the ending balance for payment 6 is -$2. Therefore, your final payment would actually be reduced by $2 to $26,903. In the real world, to prevent over paying, you should call the lender to learn the actual amount due. Beginning Amount Repayment of Principal Ending Balance Payment Payment Interest 2 3 4 6 26,905 2 Total: 161,430

Answer 1

Semi-annual Loan Payment

Loan Amount (P) = $145,750 [$182,188 x 80%]

Semi-annual Interest Rate (n) = 3% [6% x ½]

Number of period (n) = 6 Periods [3 Years x 2]

Semi-annual Loan Payment = P x {r (1+r)ⁿ} ] / [( 1+r)ⁿ – 1]

= [$145,750 x {0.03 x (1 + 0.03)⁶}] / [(1 + 0.03)³ – 1]

= [$145,750 x {0.03 x 1.194052}] / [1.194052 – 1]

= [$145,750 x 0.035821] / 0.194052

= $5,220.99 / 0.194052

= $26,905 per each semi-annual period

Loan Amortization Table

Payment	Beginning Amount	Payment	Interest Paid at 3%	Repayment of Principal	Ending Balance
1	$1,45,750	$26,905	$4,373	$22,533	$1,23,218
2	$1,23,218	$26,905	$3,697	$23,208	$1,00,009
3	$1,00,009	$26,905	$3,000	$23,905	$76,104
4	$76,104	$26,905	$2,283	$24,622	$51,482
5	$51,482	$26,905	$1,544	$25,361	$26,122
6	$26,122	$26,905	$783	$26,122	$0
TOTAL		$1,61,430	$15,680	$1,45,750	$0

Interest payment is calculated at 3% on the beginning balance of the loan.