Chandra borrows some money at 7.2%/a compounded annually. After
5 years, she repays $12 033.52 for the principal and the interest. How much
money did Chandra borrow?
P = Po(1+r)^n.
r = 7.2% / 100% = 0.072 = Annual % rate expressed as a decimal.
n = iComp/yr * 5yrs = 5 Compounding
periods.
P = Po(1.072)^5 = 12,033.52
1.41571Po = 12,033.52
Po = $8500. = Amt. borrowed.
Why did Chandra borrow money? Because money doesn't grow on trees!
To find the amount of money Chandra borrowed, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the total amount after time t
P = the principal amount (the money borrowed)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, Chandra repaid $12,033.52 after 5 years.
Plugging in the given information, we get:
12,033.52 = P(1 + 0.072/1)^(1*5)
Simplifying:
12,033.52 = P(1.072)^5
To isolate P, we divide both sides of the equation by (1.072)^5:
12,033.52 / (1.072)^5 = P
Calculating the right side, we find:
P ≈ 12,033.52 / 1.40255
P ≈ $8,580.35
Therefore, Chandra borrowed approximately $8,580.35.
To determine how much money Chandra borrowed, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (repaid amount + interest)
P = the principal amount (initial borrowed amount)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
In this case, we're given the following information:
A = $12,033.52
r = 7.2% = 0.072 (convert to decimal form)
n = 1 (compounded annually)
t = 5 years
Plugging these values into the formula, we have:
$12,033.52 = P(1 + 0.072/1)^(1*5)
Now, let's simplify the equation to solve for P:
$12,033.52 = P(1.072)^5
Next, divide both sides of the equation by (1.072)^5:
P = $12,033.52 / (1.072)^5
Using a calculator, evaluate (1.072)^5, which gives approximately 1.40255. Substitute this value into the equation:
P ≈ $12,033.52 / 1.40255
Calculating this division, we find:
P ≈ $8,582.93
Therefore, Chandra borrowed approximately $8,582.93.