Suppose that 2000 is loaned at a rate of 9% , compounded semiannually. Assuming that no payments are made, find the amount owed after 10 years.
Amount = 2000(1.045)^20
= $4823.43
Amount = 2000(1.045)^20
=
To find the amount owed after 10 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (amount owed)
P = the principal (initial loan amount)
r = the interest rate per period (as a decimal)
n = the number of compounding periods per year
t = the number of years
In this case, the principal (P) is $2000, the interest rate (r) is 9% (or 0.09 as a decimal), and the compounding periods (n) is semiannually (2 times per year). We are looking for the amount after 10 years (t = 10).
Plugging in these values into the formula, we get:
A = 2000(1 + 0.09/2)^(2*10)
Simplifying this equation:
A = 2000(1 + 0.045)^(20)
= 2000(1.045)^(20)
≈ 2000(1.48024)
Calculating further:
A ≈ $2,960.48
Therefore, the amount owed after 10 years would be approximately $2,960.48.
2000x1.66x9
=18000x166/100
=1380+2000
=(3380)x10
=33800