• # Help me please in solving the problem.

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Q:1 Why is (1+i) called an interest factor? Factoring the expression \$10,000 + 10,000 x i = 10,000 x (1+i) Thus (1+i) is an interest factor.
Q:2 You borrowed \$1,584 and must repay \$2,000 in exactly 4 years from today. Interest is compounded annually.
a. What is the interest rate [APR] of the loan? Answer 6.0%
b. What effective annual rate [EAR] are you paying? Answer 6.0%

• The formula for the compound interest is A= p(1+r)^n A is the total amount to be paid. P is the amount borrowed. r is the rate of interest. n is the year duration.
In the given example, A =2000, P= 1584, n=4 years. Now replace these values in the formula.
2000-1584(1+r)^4 that is equal to 2000/1584 = (1 + r )^4 that is equal to 1.26 =( 1+r )^4 , 1+r =1.06 so r= 1.06-1=0.06 or percentage is 6%.
The annual interest rate is 6 %.

drrao
always confident

• Q.1.
In the expression 1+i, known as interest factor, 'i' is the interest rate. As it is in percentage so for calculating it we have to use it by dividing it by 100. For example if there is an annual rate of 8% interest on your deposit of 10000 then for the first year the interest will be 10000*8/100=800. Now for the second year your principal amount is 10800 (if you do not withdraw interest) and the interest for the second year is 10800*8/100=864.
This will go on like that for subsequent years and is the basic understanding of how the compound interest is applied. The formula is based on the same logic.
Q.2.
The basic formula for compounding is -
A = P (1 + (rate in %) / 100)^n
Where A is maturity amount.
P is principal amount.
n is number of years.
^ indicates 'to the power'.

The calculations are already worked out above. You can do it yourself once again.

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