Question 1128462: Lenders such as banks, credit unions, and mortgage companies make loans. The person receiving the loan usually pays the loan off in small payments over a long period of time. The lender earns money by charging interest, which is based on a percentage of the amount that is borrowed. There are different types of interest. Car loans are usually calculated using the formula for simple interest. The total amount repaid is based on the interest and the value of the original loan, called the principal. The formula for the total dollars needed to repay the loan, with interest, is found using the formula
A=P+Pxrxt
A is the amount (total principal plus interest) required to repay the loan,
P is the amount borrowed, the principal,
r is the annual interest rate, quoted as a percent, but used as a decimal in the formula.
t is the time, in years, taken to repay the loan (six months would be 1/2 year).
Suppose you get a loan of $5,000 at an annual interest rate of 4.25%.
A. Use the given information to write the formula for the total amount to be repaid in (t) years. Express the interest rate as a decimal.
b. Complete the table of values that shows the payoff amount after certain amounts of time.
t (years) A ($)
-----------------------
0: ____ ____
4 mo: 1/3 _____
6 mo:___ _____
1 yr: ___ _____
3 yr: ___ _____
6 yr:____ _____
Estimate the maximum time allowed to repay the loan if you want the total payoff to be less than $7,000.
Please help, I've been stuck on this question forever. :( Thank you!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! this is just a matter of applying the formula.
the formule is A = P + PRT
A is the total amount of the loan that has to be paid off.
P is the principal amount loaned.
R is the interest rate per time period (years in this case).
T is the number of time periods (years in this case).
you are given:
Suppose you get a loan of $5,000 at an annual interest rate of 4.25%.
this makes P = 5000 and R = .0425.
the interest rate is the percent interest rate divided by 100.
you use the interest rate in the formula, not the percent.
4 months is 1/3 of a year.
6 months is 1/2 of a year.
your solutions are:
0: ____ ____ becomes A = 5000 + 5000 * .0425 * 0 = 5000
4 mo: 1/3 _____ bcomes A = 5000 + 5000 * .0425 * 1/3 = 5070.83 rounded to 2 decimal places.
the exact answer would be 30425/6 = 5070 + 5/6
6 mo:___ _____ becomes A = 5000 + 5000 * .0425 * 1/2 = 5106.25
1 yr: ___ _____ becomes A = 5000 + 5000 * .0425 * 1 = 5212.5
3 yr: ___ _____ becomes A = 5000 + 5000 * .0425 * 3 = 5637.5
6 yr:____ _____ becomes A = 5000 + 5000 * .0425 * 6 = 6275
for A to be equal to 7000, the formula becomes 7000 = 5000 + 5000 * .0425 * T.
solve for T to get T = (7000 - 5000) / (5000 * .0425) = 9.411764706.
when T = 9.411764706, the total amount to be paid will be equal to 7000.
any value of T less than that will result in a total payment of less than 7000.
the formula can be graphed by allowing y be equal to A and allowing T be equal to x.
here's the graph of the formula y = 5000 + 5000 * .0425 * x.
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