Consumer Mathematics and Critical Thinking Assignment (Coursework Sample)
This is a critical thinking Mathematics Assignment recently done for an engineering student for submittal for mathematical coursework. This study explains some practical examples regarding finances and interests. The terminologies being discussed are Simple Interest, Annuity earnings and mortgages along with their calculations used to find out their different parameters.source..
CONSUMER MATHEMATICS CRITICAL THINKING ASSIGNMENT
In this assignment, we discuss some practical example regarding finances and interests. We have discussed Simple Interest, Annuity earnings and mortgages explaining their calculations used to find out different parameters for these terms.
1 Simple Interest:
Simple interest is a quick and easy method to calculate the interest value on a loan amount. Simple interest is calculated by multiplying the daily interest rate r by the principal amount P by the number of days/duration t that pass between payments. The formula used to calculate Simple Interest Amount (I) is as under:
When we want to calculate the Accrued Amount (A) i.e. the Principal Amount with addition of Interest Amount, we can use formula as under:
Let’s discuss an example to explain the calculation of Simple Interest.
Mary borrowed $ 10,657.5 from her bank to build an attached garage and work space on her house. Mary’s simple interest loan had rate of 13% and required het to pay $12,250 under the agreed terms. So, we need to calculate the duration to pay her loan. So, calculate the duration, we can amend the above formula for Accrued Amount (A) as under:
* P, the principal amount is $10657.50.
* r, the interest rate is 13% per year, or in decimal form, 13/100=0.13.
So, the time duration required to play the loan amount will be 1.149-years. Usually now, the interest is added onto the principal to figure some new amount after 1.149 years.
2 Annuity Earnings:
Annuitized payouts are very important because these are the key to the retirement accounts. We start with a lump sum amount at the start of retirement, and then assume that it is being invested at a rate of return value. Then we can start to draw money out annually, for income.
The future value of an annuity is the sum of a series of periodic payments and typically involves compounding of interest as the balance increases. The formula for future value of annuity alone generally solves the question "How much will I have saved at X dollars per month after Y months."
FV of Annuity=P(1+r)n-1r
FV is the future value of annuity
P is the periodic payment
n is the number of periods
Now, let’s solve an example related to this topic as under:
Jill is saving money in an annuity and is earning 5% annual interest compounded annually. If she deposits $2,500 in the account each year for 10 years, what will the future value of the account equal? How much interest will she have earned?
Now to calculate these parameters, we can use the above formula by putting the relevant information into the formula:
FV of Annuity=2500×(1+0.05)10-10.05=$31,445
So, we can see the future value of the Jill’s account after 10 years time will be $31,445. Now we can also calculate the interest amount by subtracting the deposited total amount from future value of the Jill’s account as under:
center70104000The interest amount I will be $6,445 for 10 years annual payment to Jill’s account. The step by step variation in the annuity for a period of 10 years can be shown as under:
So, the above example clearly shows the annual variation in the amount according to the specific interest rate and hence for more period the interest amount will be more and makes more benefit to the account holder.
3 Mortgage Finances
A mortgage loan or, simply, mortgage is being used either by purchasers of real property to get finances to buy some property, or in others words by existing property owners to get finances for any requirement, while making a lien on the property which is being mortgaged. When someone borrow some money to buy a house, he signs an agreement saying that the lender has the right to take any relevant action if he can’t make their required payments on the loan. Under such consequences, the bank or lender can take the property in foreclosure — pushing him to move out of the property so that they can sell the property to pay for their debt.
The terms “mortgage” and "home loan" are most often used interchangeably. A mortgage is the formulated agreement that makes the home loan possible and not the loan itself. In real estate transactions, the agreements are need to be in writing, and a mortgage is a formulated document with specified terms and conditions that gives the lender the right to foreclose on borrower’s home.
To calculate the mortgage parameters, we
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