Suppose that $2000 is loaned at a rate of 10%, compounded semiannually. Assuming that no payments are made, find the amount owed after 5 years.

Question

Do not round any intermediate computations, and round your answer to the nearest cent

Answer 1

general formula is A=P((1+r/n)^nt

where r= interest rate, n=number of compounding periods per year, t= years, P = principle, A = Amount owed if no payments, after t years at r interest.

A = 2000(1+.1/2)^2(5)

=2000(1.05)^10

=2000(1.628894627)

= about $3,257.79

if it had been continuous compounding

A= Pe^rt = 2000e^.5 = $3,297.44 almost $40 more

the more compoundng periods per year, the greater the amount owed