Natasha plans to buy a house that cost $229,000. She has saved 20% for a down payment and plans to finance the rest. Through her local Credit Union, she has a choice of either a 20-year fixed rate loan at 3.4% or a 5/1 ARM at 3.25%.
1. How much does Natasha need to borrow? Answer
2. What is her monthly payment under the 20-year fixed option? Answer
3. What is her monthly payment under the ARM option? Answer
4. Under the 20-year fixed option, how much does she owe on the house after 5 years? Answer
5. Under the ARM option, how much does she owe on the house after 5 years? Answer
she has to borrow .8(229000) or $183,200
for Credit Union:
i = .034/12 = .0028333...
n = 20(12) = 240
paym(1 - 1.0028333..^-240)/.00283333.. = 183200
I get a paym of $1053.10 per month
balance after 5 years
= 183200(1.00283333)^60 - 1053.10(1.0028333..^60 - 1)/.0028333..
you should get $148327.00
Since I don't live in the US, I have no idea what is meant by
" a 5/1 ARM at 3.25%"
1. Natasha needs to borrow 80% of the house cost, which is $229,000 x 0.8 = $183,200.
2. Under the 20-year fixed option, her monthly payment can make her feel like she's paying for a personal comedy show. The monthly payment will be as nagging as a persistent clown, totaling around $1,274.82.
3. Under the ARM option, her monthly payment might feel like the unpredictable laughter of a circus audience. It will start at $796.54 for the first five years, but be prepared, because after that, it could jump around like a joker on a unicycle.
4. After 5 years under the 20-year fixed option, Natasha will still have a balance remaining on the house. This will make her feel like a clown attempting to juggle multiple loans. The remaining balance will be approximately $166,773.84.
5. After 5 years under the ARM option, Natasha will also have a balance remaining, continuing the circus theme of uncertainty. The remaining balance will be a surprising $198,790.94, making her wonder if she should have stayed away from the ARM loan and stuck with a solid clown car instead.
1. Natasha needs to borrow 80% of the house cost since she has saved 20% for a down payment. Therefore, the amount she needs to borrow is 80% of $229,000.
Calculation: 80% of $229,000
Answer: $183,200
2. To calculate the monthly payment under the 20-year fixed option, we can use the formula for calculating the monthly payment on a fixed-rate loan. The formula is:
Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate) ^ (-Number of Months))
Using the given interest rate of 3.4%, loan amount of $183,200, and a loan term of 20 years (240 months), we can calculate the monthly payment.
Calculation: Monthly Payment = ($183,200 * (3.4% / 12)) / (1 - (1 + (3.4% / 12)) ^ (-240))
Answer: $1,056.62
3. To calculate the monthly payment under the ARM option, we need to understand the terms of the 5/1 ARM loan. The "5/1" means that the loan has a fixed rate for the first 5 years and then adjusts annually after that. So, for the first 5 years, the ARM loan will have the same monthly payment as the fixed-rate loan.
Using the same loan amount of $183,200 and interest rate of 3.25%, we can calculate the monthly payment for the first 5 years.
Calculation: Monthly Payment = ($183,200 * (3.25% / 12)) / (1 - (1 + (3.25% / 12)) ^ (-60))
Answer: $1,019.61
4. After 5 years under the 20-year fixed option, Natasha would have made 60 monthly payments. To calculate the remaining balance on the loan, we can use an amortization formula.
The remaining balance can be calculated as:
Remaining Balance = Loan Amount * (1 + Monthly Interest Rate) ^ (-Number of Months) - (Monthly Payment * ((1 + Monthly Interest Rate) ^ (-Number of Months) - 1)) / Monthly Interest Rate
Using the loan amount of $183,200, interest rate of 3.4%, and 60 months (5 years), we can calculate the remaining balance.
Calculation: Remaining Balance = $183,200 * (1 + (3.4% / 12)) ^ (-60) - ($1,056.62 * ((1 + (3.4% / 12)) ^ (-60) - 1)) / (3.4% / 12)
Answer: $169,816.19
5. After 5 years under the ARM option, the remaining balance would still be the same as the fixed option because the ARM loan has the same monthly payment for the first 5 years. Therefore, the remaining balance on the loan after 5 years is $169,816.19.
1. To find out how much Natasha needs to borrow, we need to calculate 80% of the cost of the house, which represents the down payment she plans to make.
80% of $229,000 = 0.8 * $229,000 = $183,200
Therefore, Natasha needs to borrow $183,200.
2. To calculate her monthly payment under the 20-year fixed option, we can use a loan formula known as the Monthly Payment Formula:
M = P * ((r * (1 + r)^n) / ((1 + r)^n - 1))
Where:
M = monthly payment
P = principal amount (loan amount)
r = monthly interest rate
n = total number of monthly payments
In this case, the principal amount is $183,200, the monthly interest rate is 3.4% divided by 12 (0.034 / 12), and the total number of monthly payments is 20 years multiplied by 12 months per year (20 * 12).
Plugging in these values into the formula:
M = $183,200 * ((0.034 / 12) * (1 + (0.034 / 12))^(20 * 12)) / ((1 + (0.034 / 12))^(20 * 12) - 1)
Calculating this expression will give us the monthly payment under the 20-year fixed option.
3. To calculate her monthly payment under the ARM option, we will use the same formula as above, but with a different interest rate. In this case, the monthly interest rate is 3.25% divided by 12 (0.0325 / 12).
Using the same formula as above, but with the new interest rate, we can calculate the monthly payment under the ARM option.
4. To find out how much Natasha owes on the house after 5 years under the 20-year fixed option, we can calculate the remaining loan balance. We'll assume she makes all her payments on time and doesn't make any extra payments.
To do this, we need to calculate the number of remaining monthly payments after 5 years, which is (20 - 5) * 12 = 180 months in this case.
Using the Monthly Payment Formula with the new number of remaining monthly payments, the loan amount, and the interest rate under the 20-year fixed option, we can calculate the remaining loan balance after 5 years.
5. Similar to the calculation above, we'll find out how much she owes on the house after 5 years under the ARM option. We'll use the remaining number of monthly payments (180 months), the loan amount, and the interest rate under the ARM option to calculate the remaining loan balance.