20.09.2021

If Bobby takes out a mortgage for 30 years at an interest rate of 4% and his monthly repayments are $835.48, what is the principal loan amount?
Round your answer to the nearest ten dollars.
Do NOT round until you have calculated the final answer.

. 1

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01.10.2023, solved by verified expert
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1 students found this answer . helpful

Answer:

$148,688.73

Step-by-step explanation:

To find the principal loan amount (the initial amount borrowed), we can use the formula for calculating the monthly payment of a fixed-rate mortgage:

M = P.r.(1+r)^n / [ (1+r)^n - 1]

Where:

M is the monthly payment ($835.48)

P is the principal loan amount (what we want to find)

r is the monthly interest rate (annual interest rate divided by 12)

n is the total number of payments (number of years multiplied by 12 months)

Given:

Annual interest rate (r): 4%

Number of years (n): 30 years

First, calculate the monthly interest rate (r) by dividing the annual interest rate by 12:

r = 4% / 12 ​=0.04/12=0.003333

Now, calculate the total number of payments (n):

n =30 years×12 months/year=360 months

Now, plug these values into the mortgage payment formula and solve for P:

835.48=P x 0.003333 x (1+0.003333)^360 / [(1+0.003333)^360−1]​
 

Now, solve for P:

P≈$148,688.73

So, the principal loan amount is approximately $148,688.73 when rounded to the nearest ten dollars.
 


 

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Mathematics
Step-by-step answer
P Answered by Master

Answer:

1. $963.96

Step-by-step explanation:

Note - Since you have given multiple questions to solve, I will solve the first question for you. To get any particular question solved, please specify the question.

1) 

To calculate Tom's monthly mortgage payments, we can use the formula for a fixed-rate mortgage payment, which is:

M = P.r.(1+r)^n / [ (1+r)^n - 1]

Where:

M is the monthly payment

P is the principal amount (the remaining property value after the deposit)

r is the monthly interest rate (annual interest rate divided by 12 months)

n is the total number of payments (number of years multiplied by 12 months)

Given:

Property value (P) after the deposit: $300,000 - (0.25 * $300,000) = $225,000

Annual interest rate (r): 2%

Number of years (n): 25 years

First, calculate the monthly interest rate (r) by dividing the annual interest rate by 12:

r=2% / 12 ​=0.02/12=0.001667

Next, calculate the total number of payments (n):

n=25 years×12 months/year=300 monthsn=25 years×12 months/year=300 months

Now, plug these values into the mortgage payment formula:

M=$225,000 x 0.001667x (1+0.001667)^300​  / [(1+0.001667)^300−1]
 

Calculating this expression will give us Tom's monthly mortgage payment: M≈$963.96

So, Tom's monthly mortgage payment will be approximately $963.96 when rounded to the nearest cent.


 

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m=mass

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The solution is given in the image below
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Here,

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time=1sec

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Left wood=6 feet

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Picture frame built till now= 6/(3/4)

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Therefore, till now 8 pieces have been made.

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here,

L=12.4 cm

b= 8.8 cm

A= L*b

= 12.4 * 8.8 = 109.12 cm^2

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