An amount of
$20,000
is borrowed for
13
years at
5%
interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?
20000 * 1.05^13
To find out how much must be paid back, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (amount to be paid back)
P = the principal amount borrowed ($20,000)
r = the annual interest rate (5% or 0.05 as a decimal)
n = the number of times the interest is compounded per year (annually, so 1)
t = the number of years (13)
Plugging in the values into the formula:
A = 20000(1 + 0.05/1)^(1*13)
Simplifying:
A = 20000(1 + 0.05)^13
Using a calculator or a spreadsheet, we calculate the value inside the parenthesis first: (1 + 0.05)^13 = 1.93505.
Then, we multiply this value by the principal amount:
A = 20000 * 1.93505
A = 38,701
Therefore, at the end of the 13-year period, $38,701 must be paid back.