Rachel Spender wants to invest $4000 in savings certificates which bear an interest rate of 7.25% compounded semi-anually. How long a time period should she choose in order to save an amount of $4700? ***************************************************** Future-value-of-$1 formula:, with = Future Value (Unknown, in this case) = Principal/Initial Deposit ($4,000, in this case) = Interest rate, as a decimal (7.25%, or .0725, in this case) = Number of ANNUAL compounding periods (semiannually, or 2, in this case) = Time Principal/Initial Deposit has been invested, in YEARS (t, in this case) How long a time period should she choose in order to save an amount of $4700? ----- Substituting $4,700 for A, $4,000 for P, .0725 for i, and 2 for m ----- Converting to LOGARITHMIC form Time it'll take the $4,000 investment to increase to $4,700, or = 2.26446601 years, which needs to be ROUNDED UP to years, or 2 years, 6 months. ** Notice that although 2.26446601 rounds off to about years, the $4,000 investment, at the -year juncture, will increase to about $4,695.16 (< $4,700). This is why it's necessary to ROUND UP to year , or 2.5 years (at the semi-annual point), at which time, the $4,000 initial deposit will exceed $4,700 (about $4,779.50, to be exact).