An amount of
$27,000
is borrowed for
6
years at
8.25%
interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?
i = .0825
n = 6
amount = 27000(1.0825)^6
= .....
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778
To calculate the amount that must be paid back, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial loan)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case:
P = $27,000
r = 8.25% = 0.0825 (converted to decimal)
n = 1 (interest compounded annually)
t = 6 years
Now we can plug these values into the formula and solve for A:
A = 27000(1 + 0.0825/1)^(1*6)
A = 27000(1 + 0.0825)^(6)
A ≈ 27000(1.0825)^(6)
A ≈ 27000(1.609356)
A ≈ $43,547.82
Therefore, the amount that must be paid back at the end of the 6-year period is approximately $43,547.82.