Question

You invest $100,00 in an account with an annual interest rate of 4.5% , compounded semiannually. How much money will you have in the account after 10 years? Round your answer to the nearest whole number.

Answer 1

This formula is a little more complicated because we are compounding 2 times a year.  The formula is: A(t) = P(1+[r/n])^(t)(n), where A(t) is the final amount, P is the initial investment, r is the rate, n is the NUMBER of times the interest compounds per year, and t is the time in years. Our particular formula would be filled in like this: A(t)= 100(1+[.045/2])^(10)(2). Simplify the fraction there first:
A(t) = 100(1+.0225)^(10)(2).  Then inside the parenthesis: A(t)=100(1.0225)^(10)(2).  Now multiply the 10*2 to get A(t)=100(1.0225)^20. Take 1.0225 to the 20th to get A(t)=100(1.5605) and finish by multiplying that result by 100: A(t) = $156.05.  Usually it's the "n" that throws people off; they are not sure which formula to use for it or they use the wrong value.