Waleed just purchased a new house for N$120,000. He was able to make a down payment equal to 25% of the value of the house; the balance was mortgaged. The rate by the bank is 10% compounded annually. The mortgage has a 20-year amortization period (this means that payments are calculated assuming it will take 20 years to pay off the loan). Determine the size of the payments and the balance on the mortgage after 5 years
Question
Waleed just purchased a new house for N$120,000. He was able to make a down payment equal to 25% of the value of the house; the balance was mortgaged. The rate by the bank is 10% compounded annually. The mortgage has a 20-year amortization period (this means that payments are calculated assuming it will take 20 years to pay off the loan). Determine the size of the payments and the balance on the mortgage after 5 years
Solution
First, let's calculate the amount that was mortgaged. Waleed made a down payment of 25% on the N$120,000 house.
25% of N30,000
So, the amount that was mortgaged is the total cost of the house minus the down payment.
N30,000 = N$90,000
Next, let's calculate the size of the annual payments. The formula for the annual payment (PMT) on a mortgage is:
PMT = P * r * (1 + r)^n / ((1 + r)^n - 1)
where: P = principal amount (the amount that was mortgaged) r = annual interest rate divided by the number of periods per year n = total number of payments (or periods)
In this case, P = N$90,000, r = 10% or 0.10 (compounded annually, so we don't need to divide it), and n = 20 years.
PMT = 90,000 * 0.10 * (1 + 0.10)^20 / ((1 + 0.10)^20 - 1) PMT = N$8,718.41
So, the size of the annual payments is N$8,718.41.
Finally, let's calculate the balance on the mortgage after 5 years. The formula for the balance (B) of a loan after a certain number of payments is:
B = P * (1 + r)^n - PMT * ((1 + r)^n - 1) / r
In this case, we want to find the balance after 5 years, so n = 5.
B = 90,000 * (1 + 0.10)^5 - 8,718.41 * ((1 + 0.10)^5 - 1) / 0.10 B = N$75,395.41
So, the balance on the mortgage after 5 years is N$75,395.41.
Similar Questions
A home was bought with a 20%20% down payment of R177175,00R177175,00. The balance was financed for 2020 years at 9,4%9,4% interest per annum, compounded semi-annually. Find the size of the half-yearly payments for the loan.
Simon has taken a 20-year, $252,000 mortgage on his house at an interest rate of 6% p.a., compounded annually. What is the remaining balance of the mortgage after the payment of the fifth annual instalment?
The Henley's took out a loan for $195,000 to purchase a home. At a 4.3% interest rate compounded annually, how much will the loan be after 5 years?
A person purchased a $180477 home 10 years ago by paying 15% down and signing a 30-year mortgage at 9.3% compounded monthly. Interest rates have dropped and the owner wants to refinance the unpaid balance by signing a new 20-year mortgage at 6% compounded monthly How much interest will refinancing save? Money Saved =?
The Murphys bought a $371,000 townhome. They made a down payment of $44,000 and took out a mortgage for the rest. Over the course of 15 years they made monthly payments of $2759.42 on their mortgage until it was paid off.(a) What was the total amount they ended up paying for the townhome (including the down payment and monthly payments)?$(b) How much interest did they pay on the mortgage?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.