Amanda Vehicle has hired Jared Frost as its new president. Terms included the company’s agreeing to pay retirement benefits of $
17,900 at the end of each semiannual period for 12 years. This will begin in 4,015 days. If the money can be invested at 8% compounded semiannually, what must the company deposit today to fulfill its obligation to Robert?
The amount needed in the account when Frost retires is given by the annuity formula. Compounding is 2 times per year. .. A = Pi/(n(1 -(1 +r/n)^(-nt))) .. 17900 = P*.08/(2*(1 -(1 +.08/2)^(-2*12))) .. 17900 = P*.04/(1 -(1.04^-24)) .. P ≈ 272,920.64
The compound interest formula can be used to find the present value required. 4015 days is 11 years (ignoring leap years), so the amount to deposit can be calculated from .. A = P*(1 +r/n)^(nt) .. 272,920.64 = P*(1 +.08/2)^(2*11) = P*1.04^22 .. P ≈ 115,160.33
We don't know about the company's obligation to Robert. To fulfill its obligation to Frost, it must deposit 115,160.33 today.
