Question

Suppose that P dollars is invested in a savings account at interest rate I, compounded semiannually, for one year. The amount A in the account after one year is given by A = P(1 + i/2)^2

I got help with a problem similar to this earlier, but I still do not understand.

Thank you! :-)

Answer 1

interest rate is i per year
so it is i/2 for half a year
every half hear you multiply by (1+i/2)
so after 1 year, two half years, you multiply by (1+/2)(1+i/2) = (1+i/2)^2

say i = 20% = .20
that is 10% per half year or .10 added every half year
so after a half year we have P + .10 P = P(1.10)
after a whole year, multiply by (1.1 again
P (1.10)^2 = 1.21 P